Hydraulics

Explanation: A substance that can flow and take the shape of its container is known as a fluid. Liquids and gases are both considered fluids as they can deform continuously under the action of shear stress, unlike solids which generally have a defined shape and resist deformation.

Explanation: Practical fluids, including both liquids and gases, typically possess viscosity, surface tension, and compressibility. Viscosity refers to the resistance of a fluid to flow, surface tension is the force acting on the surface of a liquid that causes it to minimize its surface area, and compressibility is the ability of a fluid to decrease in volume under pressure.

Explanation: An ideal fluid is a theoretical concept used in fluid dynamics. It is considered to be frictionless and incompressible, meaning it has no internal friction and does not change in volume under external pressure. While it serves as a useful theoretical model, real-world fluids do not perfectly exhibit these characteristics.

Explanation: Liquids or fluids do not have their own shape and take the shape of the container they are placed in. This is one of the fundamental characteristics that distinguishes fluids from solids, which have a definite shape and volume.

Explanation: Liquids do not have a definite shape and take the shape of the container they are in. They can be compressed, although the degree of compressibility varies depending on the specific properties of the liquid. Liquids are also affected by changes in pressure and temperature, so option (c) is not accurate.

Explanation: The variation in the volume of a liquid when subjected to changes in pressure is known as compressibility. This property refers to how easily the volume of a substance can be reduced when pressure is applied to it. Liquids generally have low compressibility compared to gases.

Explanation: Mass density (ρ) is defined as the mass of a substance per unit volume. It is calculated by dividing the mass of the substance by its volume. The formula for mass density is ρ = mass / volume.

Explanation: Poise is a unit used to measure dynamic viscosity. It is named after the French physician Jean Léonard Marie Poiseuille. The unit measures the internal friction or resistance to flow within a fluid, often a liquid. It is commonly used in the field of fluid dynamics and rheology.

Explanation: Stoke is a unit used to measure kinematic viscosity, which is the ratio of dynamic viscosity to density. It is named after the British physicist and mathematician Sir George Gabriel Stokes. The unit is commonly used in the context of fluid dynamics and the study of flow patterns in liquids and gases.

Explanation: To convert one poise (unit of dynamic viscosity) into the MKS (Meter-Kilogram-Second) unit of dynamic viscosity, the multiplying factor is 0.1. This means that one poise is equivalent to 0.1 pascal-second (Pa·s), which is the MKS unit for dynamic viscosity.

Explanation: The specific weight of a liquid, defined as the weight per unit volume of the liquid, does not vary on any other planet except Earth. This is because specific weight is dependent on gravitational acceleration, which varies from one celestial body to another.

Explanation: The specific weight of water is 1000 kg/m^3 under standard conditions, which include normal atmospheric pressure of 760 mm of mercury, a temperature of 4°C, and measurement at mean sea level. All these conditions are typically considered when specifying the specific weight of water.

Explanation: The specific weight of sea water is higher than that of pure water primarily due to the presence of dissolved salts, as well as dissolved air and suspended matter. These additional components contribute to the overall weight per unit volume of sea water, making it denser than pure water.

Explanation: The specific gravity of a substance is defined as the ratio of its density to the density of a standard substance, typically water. In this case, the specific gravity would be 0.75, indicating that the liquid is lighter than water.

Explanation: Water is considered a Newtonian fluid because its viscosity remains constant regardless of the applied shear stress. In other words, the rate of deformation is directly proportional to the shear stress for Newtonian fluids, and water exhibits this behavior under normal conditions.

Explanation: Hooke’s law, which describes the behavior of an elastic material, is analogous to Newton’s law of viscosity for fluids. Hooke’s law states that the strain in a solid material is directly proportional to the stress applied to it within the elastic limit, while Newton’s law of viscosity similarly relates shear stress to the rate of deformation in fluids.

Explanation: The viscosity of liquids typically decreases as the temperature increases. This relationship between viscosity and temperature is inverse, meaning that as the temperature rises, the viscosity of the liquid decreases. Conversely, as the temperature decreases, the viscosity tends to increase.

Explanation: Unlike liquids, the viscosity of gases is directly proportional to temperature. As the temperature of a gas increases, its viscosity also increases, and vice versa. This relationship is an important consideration in the study of fluid dynamics and the behavior of gases.

Explanation: Surface tension is the force acting on the surface of a liquid that causes it to minimize its surface area and behave like an elastic membrane. It is commonly measured as the force per unit length. Surface tension is responsible for the formation of droplets and the unique behavior of liquids at the surface.

Explanation: When drops of water fall, they tend to form spherical shapes due to the cohesive forces between water molecules and the surface tension of the liquid. Surface tension acts like a thin, elastic skin on the surface of the water, minimizing the surface area and causing the drops to assume a spherical shape.

Explanation: In an open tube, the free surface of a liquid, such as mercury, curves upwards due to the phenomenon of surface tension. The surface tension of the liquid causes it to adhere to the walls of the tube, leading to a curved meniscus. This is commonly observed in open tubes filled with liquids like mercury or water.

Explanation: When using a level pipe for leveling, the level is indicated by the upper face of the liquid in the pipe. The upper surface of the liquid in the pipe serves as a reference point for determining the level of the ground or other surfaces being measured. This method is commonly employed in surveying and construction work.

Explanation: The pressure difference between the inside and outside of a droplet of water is given by 4σ/d, where σ represents the surface tension of the liquid and d is the diameter of the droplet. This relationship explains the pressure differential that contributes to various phenomena, such as capillary rise or fall, observed in small-diameter tubes or droplets.

Explanation: The phenomenon of the rising of a liquid surface in a tube of small diameter relative to the adjacent normal level of the liquid is known as capillary rise. This effect occurs due to the combined forces of adhesion, cohesion, and surface tension. Capillary rise is commonly observed in thin tubes or pores, where the liquid defies gravity and ascends higher than the normal surface level.

Explanation: Capillary rise is directly proportional to the surface tension of the liquid. Surface tension plays a critical role in determining the height to which the liquid can rise in a small-diameter tube or capillary. The stronger the surface tension, the greater the capillary rise observed in the tube.

Explanation: Capillarity of water is influenced by various factors, including surface tension, the angle of contact, and the diameter of the pipe. These parameters collectively impact the extent of capillary action exhibited by water in thin tubes or capillaries. Capillarity is directly related to surface tension and inversely related to both the angle of contact and the diameter of the tube.

Explanation: The capillary rise or fall of a liquid is determined by the equation h = 4σ cos θ / ρgd, where h represents the height of the rise or fall, σ is the surface tension, θ is the angle of contact, ρ is the density of the liquid, g is the acceleration due to gravity, and d is the diameter of the tube. This formula allows for the calculation of the extent of capillary action observed in various situations.

Explanation: Using the given data and the formula for capillary rise or fall, the calculated value is 0.393 cm, indicating the capillary rise in the glass tube when immersed in mercury. This demonstrates the extent to which the surface tension and other factors contribute to the phenomenon of capillarity in various liquids.

Explanation: The rise or fall of a liquid in a glass tube of a small diameter when dipped is inversely proportional to the diameter of the glass tube. This suggests that the smaller the diameter of the tube, the greater the capillary action observed, leading to a more significant rise or fall of the liquid. The extent of the capillary action is influenced by the size of the tube.

Explanation: Pascal’s law states that pressure at a point in a fluid at rest is transmitted equally in all directions. This principle applies to fluids in equilibrium, implying that the pressure at any point within the fluid is the same in all directions. Pascal’s law is fundamental in understanding the behavior of fluids in various contexts, such as hydraulic systems and fluid mechanics.

Explanation: The pressure at a depth of 5 cm is zero, as there is no water above this point. At a depth of 15 cm, the pressure exerted is 50 kg/m^2. These values are obtained by considering the density of water and the gravitational acceleration, as per the principles of hydrostatics.

Explanation: The concept that a liquid transmits pressure equally in all directions when pressure is applied to its surface is attributed to Pascal’s law. This fundamental principle in fluid mechanics helps explain the behavior of fluids under various conditions and is instrumental in the design and operation of hydraulic systems.

Explanation: The continuity equation is primarily concerned with the law of conservation of mass in fluid mechanics. It relates to the principle that mass cannot be created or destroyed in a fluid flow system, emphasizing the balance between the mass inflow and outflow at any point in the system.

Explanation: The equation of continuity of fluids is applicable when the flow is steady, incompressible, and one-dimensional. These conditions are necessary for the equation to accurately describe the conservation of mass in a fluid flow system and to ensure the validity of the fluid dynamics principles involved.

Explanation: The continuity equation in fluid dynamics is concerned with the relationship between the momentum per unit volume between two points on a streamline. It helps describe the behavior of fluids in terms of their mass and momentum flow rates and serves as a fundamental tool in analyzing and understanding fluid dynamics principles.

Explanation: An ideal flow of a liquid adheres to the continuity equation, which describes the conservation of mass in the flow system. The continuity equation is essential in understanding the behavior of fluids and plays a significant role in the study of fluid dynamics and related phenomena.

Explanation: Atmospheric pressure is commonly measured using barometers, which are instruments designed specifically for this purpose. Barometers help determine the pressure exerted by the Earth’s atmosphere, providing valuable information for weather forecasting and other atmospheric studies.

Explanation: The pressure less than atmospheric pressure can be referred to as suction pressure, vacuum pressure, or negative pressure, depending on the context and the specific application. These terms are used interchangeably to describe pressure conditions below the atmospheric pressure level.

Explanation: The atmospheric pressure experiences variations primarily with changes in altitude. As the altitude increases, the atmospheric pressure decreases, leading to changes in atmospheric conditions and weather patterns. Understanding these variations is essential for various fields, including meteorology and aviation.

Explanation: Gauge pressure refers to the pressure measured relative to the atmospheric pressure, usually denoted as the difference between the absolute pressure and the atmospheric pressure. This type of pressure measurement is commonly used in various applications, including the calibration of pressure gauges and instruments.

Explanation: Barometers are primarily used to measure atmospheric pressure. These instruments are designed to provide a direct indication of the pressure exerted by the Earth’s atmosphere at a specific location. Barometric pressure measurements are important for weather forecasting and related atmospheric studies.

Explanation: Manometers are typically used to measure pressure in various fluid systems, such as water channels, pipes, or industrial equipment. They are valuable tools for determining the pressure within a closed system or fluid-carrying components.

Explanation: Differential manometers are specialized pressure measurement instruments used to determine the difference in pressure between two points within a system. They are particularly useful in applications where pressure variations between specific locations need to be assessed.

Explanation: Piezometers are instruments designed for measuring very low pressures, such as those found in geotechnical engineering or soil mechanics. They are used to monitor and assess pore water pressures in soil or rock formations, making them valuable tools in the field of civil and geotechnical engineering.

Explanation: In the context of fluid flow within pipes, the pressure is typically greater than atmospheric pressure. This increased pressure is a result of the energy imparted to the fluid to maintain its flow through the pipe network. It is essential for conveying fluids through pipelines, whether for water supply, gas distribution, or other industrial applications.

Explanation: Micro manometers are specialized instruments designed to accurately measure low pressures with a high degree of precision. They are used in various applications where precise measurement of low-pressure differentials is crucial, such as in laboratories and scientific research.

Explanation: The total pressure exerted on the top of a closed cylindrical vessel filled with liquid is directly proportional to the fourth power of the radius. This relationship is derived from hydrostatic principles and is significant in various engineering and fluid mechanics applications.

Explanation: Molecules of fluids are attracted to other surfaces or materials due to a phenomenon known as adhesion. Adhesion occurs when the molecules of a fluid adhere to the molecules of a solid surface, creating intermolecular forces at the interface between the fluid and the solid. This plays a crucial role in capillary action and surface tension phenomena.

Explanation: Cohesion refers to the attraction among particles of the same material. It is the force that holds particles of the same substance together and creates the property of surface tension in liquids. Cohesion is essential in understanding the behavior of fluids and their interactions.

Explanation: The concept of “1 m head” refers to the pressure exerted by a column of fluid that is 1 meter in height. This pressure is equivalent to 0.1 kg/cm^2, and it is a fundamental unit used in fluid mechanics and hydrostatics to measure pressure based on the height of a fluid column.

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Explanation: Not available.

Explanation: The height of an oil column can be determined using the relationship between pressure, specific gravity, and fluid column height. In this case, the specific gravity of oil is 0.7, and the pressure is 0.14 kgf/cm^2, which corresponds to a height of 2 meters (200 cm) of oil.

Explanation: Specific gravity (SG) is defined as the ratio of the density of a substance to the density of a reference substance (usually water). If the specific gravity of oil is 0.7, the density of the oil can be calculated as 700 kg/cm^3 since the density of water is approximately 1000 kg/cm^3.

Explanation: The pressure difference (head) in a mercury-oil differential manometer can be calculated using the height difference of the mercury levels and the specific gravity of the oil. In this case, with a 20 cm difference in mercury level and a specific gravity of oil equal to 0.8, the pressure head corresponds to 3.20 meters of oil.

Explanation: Specific gravity (SG) is defined as the ratio of the density of a substance to the density of water. If the volume of liquid weighing 3000 kg is 4 cubic meters, the density of the liquid is 750 kg/m^3. To find the specific gravity, divide the density of the liquid by the density of water (approximately 1000 kg/m^3). Therefore, SG = 750 kg/m^3 / 1000 kg/m^3 = 0.75.

Explanation: A stream line is an imaginary line that is drawn such that the tangent at any point along the line indicates the direction of the velocity of a fluid particle at that point. Streamlines help visualize the flow pattern of a fluid and are commonly used in fluid dynamics and fluid mechanics.

Explanation: In fluid dynamics, steady flow refers to a condition where the flow parameters, including velocity, pressure, and density, do not change with time at a specific point in a fluid. It is characterized by the constancy of flow conditions and is essential for the analysis of fluid systems.

Explanation: Uniform flow in a fluid system occurs when the size and shape of the cross-section remain constant along a particular length of a channel or pipe. This uniformity in cross-section results in constant flow parameters, such as velocity, making it a key concept in fluid dynamics.

Explanation: When the velocity, pressure, density, and other flow parameters at a specific point in a fluid do not change with respect to time, the flow is referred to as steady flow. Steady flow conditions signify that the fluid properties at that point remain constant over time.

Explanation: Unsteady flow, also known as transient flow, occurs when the velocity, pressure, density, or other flow properties at a specific point in a fluid change with respect to time. This type of flow is characterized by time-dependent variations in fluid properties.

Explanation: Uniform flow occurs when the velocity of fluid particles remains constant with respect to the length of the flow direction. In this type of flow, the fluid maintains a constant velocity profile along its path.

Explanation: The description provided does not specify a particular type of flow, so there is no clear classification based on the information given.

Explanation: Incompressible flow is characterized by the constancy of fluid density from point to point within a flow region. The property of incompressibility assumes that the density of the fluid does not vary significantly under the prevailing flow conditions.

Explanation: Compressible flow refers to the type of flow where the density of the fluid varies from point to point within a flow region. This variation in density implies that the fluid is compressible, and its density can change under the influence of pressure and temperature fluctuations.

Explanation: Turbulent flow is characterized by irregular fluctuations in the velocity of fluid particles, which occur from point to point in both magnitude and direction. Turbulent flow is distinct from laminar flow, and it is often associated with chaotic and unpredictable fluid motion.

Explanation: Turbulent flow is marked by the crossing of individual fluid particles’ paths, resulting in complex and erratic fluid motion. This type of flow is commonly observed in situations where the flow velocity exceeds a critical value, leading to the disruption of smooth fluid motion.

Explanation: In the context of a steady uniform flow through a long pipe, the flow rate remains constant, implying that the flow velocity and fluid properties do not change along the length of the pipe. This type of flow is essential for efficient and stable fluid transportation.

Explanation: Stream line flow refers to the type of flow where each liquid particle follows a distinct and well-defined path as it moves through the fluid medium. Stream lines help visualize the flow pattern and aid in understanding fluid behavior and characteristics.

Explanation: In open channel flow, the Froude number is a dimensionless parameter that describes the flow regime based on the balance between inertial and gravitational forces. When the Froude number is less than 1.0, the flow is referred to as sub-critical, indicating that the flow is controlled primarily by gravity, and the flow depth is less significant than the wave speed.

Explanation: When the Froude number in open channel flow is precisely 1.0, the flow is referred to as critical flow. In this state, the flow characteristics change, and the transition from sub-critical to super-critical flow occurs, resulting in specific hydraulic behaviors and conditions.

Explanation: When the Froude number in open channel flow exceeds 1.0, the flow is denoted as shooting flow. This condition signifies that the flow is super-critical, indicating that wave speed is significant and is influenced by inertial forces more than gravitational forces.

Explanation: Laminar flow refers to the type of flow where fluid particles move in layers parallel to the boundary or surface. This orderly motion occurs in a smooth and predictable manner, without significant intermixing between adjacent layers of fluid.

Explanation: Laminar flow is characterized by the orderly movement of fluid particles in straight paths, where all the streamlines are parallel to the surface or boundary. This type of flow exhibits smooth and predictable fluid behavior.

Explanation: Turbulent flow is associated with higher fluid losses due to increased energy dissipation resulting from the chaotic and irregular motion of fluid particles. The turbulent nature of the flow leads to enhanced frictional losses and increased energy expenditure within the fluid system.

Explanation: Laminar flow can be observed in various scenarios, including underground flow and flow past tiny bodies, where the fluid motion occurs in well-defined layers parallel to the boundary. These examples exhibit the smooth and regular motion characteristic of laminar flow.

Explanation: Turbulent flow is characterized by the irregular and chaotic movement of fluid particles, leading to a zig-zag motion within the fluid medium. This type of flow is known for its unpredictable behavior and increased fluid mixing and intermixing.

Explanation: In a flowing liquid, a fluid particle can possess different forms of energy, including potential energy, kinetic energy, and pressure energy. These energy forms are essential in understanding the dynamics and behavior of fluid particles within a fluid system.

Explanation: Bernoulli’s equation is based on several fundamental assumptions, including the non-viscous nature of the fluid, fluid homogeneity, and the flow occurring along the streamline. These assumptions help simplify the fluid dynamics analysis and aid in understanding fluid behavior in various applications.

Explanation: The main assumption of Bernoulli’s equation encompasses various factors, including the uniform velocity of liquid particles across any cross-section of a pipe, the absence of external forces except gravity, and the absence of energy loss in the liquid during flow. These assumptions are crucial for the application and derivation of Bernoulli’s equation in fluid dynamics and engineering.

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Explanation: Bernoulli’s theorem is primarily concerned with the conservation of energy within a fluid flow system. It states that the total energy in a fluid flow system remains constant along a streamline, emphasizing the interplay between potential energy, kinetic energy, and pressure energy within the fluid.

Explanation: The total head of a particle in motion involves the summation of various energy components, including potential head, kinetic head, and pressure head. These energy components collectively represent the total energy possessed by the fluid particle within a fluid flow system.

Explanation: The term v^2/2g is recognized as the kinetic energy per unit weight, representing the energy possessed by the fluid particle due to its motion. This term is a crucial component of the total energy equation and contributes to the overall energy balance within the fluid system.

Explanation: The term z represents the potential energy per unit weight, signifying the energy possessed by the fluid particle due to its elevation or height within the gravitational field. This term contributes to the total energy equation and helps evaluate the overall energy distribution within the fluid system.

Explanation: The term P/pg denotes the pressure energy per unit weight, representing the energy possessed by the fluid particle due to its pressure within the fluid system. This term contributes to the overall energy balance and aids in understanding the pressure distribution within the fluid flow.

Explanation: The energy possessed by a fluid due to its pressure within the fluid system is referred to as elevation energy. This type of energy is crucial in understanding the pressure distribution and the overall energy dynamics within the fluid flow system.

Explanation: In a fluid flow, the liquid particles can possess various forms of energy, including potential energy, kinetic energy, and pressure energy. These energy forms contribute to the overall energy balance and aid in understanding the energy distribution and dynamics within the fluid system.

Explanation: An independent mass of fluid does not possess pressure energy. While the fluid may possess other forms of energy, such as elevation energy and kinetic energy, the concept of pressure energy is not applicable to an independent mass of fluid.

Explanation: The line that connects the points to which the liquid rises in vertical piezometer tubes at different cross-sections of a conduit is known as the piezometric line. This line provides essential information about the pressure distribution and the flow dynamics within the fluid system.

Explanation: The hydraulic gradient line (H.G.L.) represents the sum of the pressure head and datum head within a fluid flow system. This line serves as a crucial indicator of the pressure distribution and the energy dynamics along the length of the flow path.

Explanation: The total energy line (T.E.L) represents the sum of the pressure head, kinetic head, and datum head within a fluid flow system. This line aids in understanding the overall energy distribution and dynamics, offering insights into the energy balance within the fluid system.

Explanation: The difference between the total energy line and the hydraulic gradient line corresponds to the kinetic head, signifying the energy lost due to the fluid’s motion within the system. This loss of energy is a crucial factor in understanding the energy dynamics and losses within the fluid flow system.

Explanation: Pressure head is represented by the term P/w, where P denotes pressure and w represents the specific weight of the fluid. This term serves as a vital component in the evaluation of the energy distribution and pressure dynamics within the fluid flow system.

Explanation: The difference between the total energy gradient line and the total energy line corresponds to the loss of head within the fluid flow system. This loss of energy is an essential factor in understanding the energy dynamics and losses occurring during the fluid flow process.

Explanation: The imaginary line that connects each head of water within a fluid flow system is known as the hydraulic gradient line. This line aids in understanding the energy distribution and pressure dynamics along the flow path, providing crucial insights into the flow behavior and characteristics.

Explanation: The hydraulic gradient line and total energy line are distinct and represent different aspects of the energy distribution and dynamics within a fluid flow system. While both lines offer valuable insights into the flow behavior, they correspond to different energy components and serve different analytical purposes.

Explanation: The hydraulic gradient line for an open flow channel remains at the same level as the water level within the channel. This line represents the energy distribution and dynamics within the open flow channel, providing valuable information about the pressure and energy balance along the flow path.

Explanation: The hydraulic gradient line, except in the case of a siphon, remains positioned above the centerline of the conduit. This line helps in understanding the pressure distribution and energy dynamics within the fluid flow system, providing insights into the overall flow behavior.

Explanation: The head of water represented in the case of the hydraulic gradient line (HGL) is known as the residual head. This head corresponds to the remaining or leftover energy within the fluid flow system and aids in understanding the energy balance and flow characteristics.

Explanation: The hydraulic gradient represents the total loss of head due to friction and other factors in a fluid flow system divided by the total length of the channel. It is a critical parameter for understanding the energy distribution and losses in the flow.

Explanation: All the provided statements are correct. The total energy gradient graphically represents the total head at any section of a pipeline. The vertical distance between the total energy line and the hydraulic grade line equals the velocity head, and the vertical distance between the total energy line and the total energy gradient represents the loss of head.

Explanation: The specific energy of a flowing fluid per unit weight is calculated as (v^2/2g) + h, where v represents velocity, g is the acceleration due to gravity, and h is the elevation head. It quantifies the total energy per unit weight for the fluid.

Explanation: Conjugate depths refer to the two depths at which the specific energy of a flowing fluid is the same. These depths play a critical role in the study of open channel flow and hydraulic structures.

Explanation: The velocity of approach (v_a) is calculated as the ratio of the discharge over the notch to the area of the channel. It is an important parameter in the study of flow over weirs and notches.

Explanation: The hydraulic coefficient for orifices, C_d, is equal to the product of the coefficients C_c and C_v. This relationship is fundamental for calculating the discharge characteristics of orifices.

Explanation: A weir with end contraction typically has a width that is less than the width of the channel in which it is installed. The end contraction allows for more accurate flow measurement and control.

Explanation: The upper surface of the notch over which water flows is known as the sill. This is a critical component in weirs and notches and influences the flow characteristics.

Explanation: When the crest of a weir is lower than the downstream water level, it is referred to as a submerged weir. This configuration has specific applications in hydraulic engineering.

Explanation: A Cipolletti weir is a type of trapezoidal weir with a specific side slope configuration where the horizontal (H) to vertical (V) ratio is 1:4. This design is used for flow measurement and control in open channels.

Explanation: The discharge (Q) over a rectangular weir can be calculated using any of the provided equations. These equations are all valid for calculating the discharge, depending on the specific parameters and coefficients used.

Explanation: The notch formula is used to calculate the discharge (Q) over a weir or notch. The formula, as given, is a common expression used for this purpose.

Explanation: To limit the rise of water above the crest to a specific level, you can calculate the required length of the weir. In this case, with a discharge of 5.00 m^3/sec and Cd = 0.62, the length of the weir should be 2.73 meters to ensure that the water does not rise more than 100 cm above the crest.

Explanation: The velocity of approach (V_a) is calculated as Q/L(H+L), where Q is the discharge, L is the length of the weir, H is the head of water over the weir, and S is the height of the crest above the base of the channel. This parameter is important for understanding the flow conditions.

Explanation: A clinging nappe in a weir configuration typically results in excess discharge compared to a free-flowing nappe. The excess discharge can be in the range of 25% to 30%, making it important to consider in weir design and flow calculations.

Explanation: The discharge through a triangular notch can be calculated using the given formula, where Cd represents the coefficient of discharge, g is the acceleration due to gravity, H is the head of water over the notch, and θ is the angle of the notch.

Explanation: The notch angle for achieving the maximum discharge over a triangular notch is 90 degrees (a right-angle triangle). This configuration is essential for accurately measuring flow rates.

Explanation: Triangular notches are preferred over rectangular notches, especially for low discharge rates (Q≤100m^3/sec), because they provide more accurate results in this flow range.

Explanation: The formula for the discharge through a Cipolletti weir is as given, where Cd represents the coefficient of discharge, L is the length of the weir, g is the acceleration due to gravity, and H is the head of water over the weir.

Explanation: The discharge through a V-notch weir varies as the fifth power of the head (H^5/2). This relationship is essential to understand when designing and using V-notch weirs for flow measurement.

Explanation: A stepped notch is typically composed of rectangular notches of different sizes. This configuration allows for the measurement of different flow rates accurately and with precision.

Explanation: The ratio of the percentage error in the discharge and the percentage error in the measurement of head over a rectangular notch is 3/2. This relationship is important to consider when assessing the accuracy of measurements.

Explanation: The ratio of the percentage error in the discharge and the percentage error in the measurement of head over a triangular notch is 5/2. This relationship is crucial for understanding the precision and accuracy of measurements.

Explanation: According to Francis’ formula, the effect of end contraction on each side is 0.1 times the height of the liquid above the sill (0.1H). Understanding this effect is important for accurate calculations and measurements.

Explanation: The discharge passing through the crest can be calculated using the provided parameters and the appropriate formula. In this case, the discharge is 0.0160 cm³/sec.

Explanation: A Cipolleti weir is a type of trapezoidal weir with specific side slope dimensions. Its configuration allows for accurate flow measurement and control.

Explanation: The thickness of a sharp-crested weir is typically kept less than half the height of water on the sill. This design consideration ensures proper flow measurement and control.

Explanation: The discharge over an ogee weir remains the same as that over a Cipolleti weir. This is an important aspect to consider when designing and using these types of weirs for flow measurement.

Explanation: The pressure difference at the two ends of an inclined pipe can be attributed to various factors, including sudden head drops at the inlet, exit head drops, and frictional loss head. Understanding these factors is crucial for fluid flow analysis and calculations.

Explanation: A rotameter is a device commonly used for measuring the discharge of fluids. It operates based on the principle of variable-area flow meters and is widely utilized in various industrial and laboratory settings for flow measurement purposes.

Explanation: Venturimeter is a device specifically used to measure the rate of flow of fluids in a pipe. It operates based on the principle of the Venturi effect, which results in a pressure drop and an increase in the flow velocity as the fluid passes through the constriction in the device.

Explanation: In the design of a venturimeter, the divergent cone is maintained at the same length as the convergent cone. This ensures a gradual transition of the fluid from the high-velocity, low-pressure zone to the low-velocity, high-pressure zone.

Explanation: Typically, the inlet length of a venturimeter is shorter than the outlet length. This configuration enables the smooth and efficient transition of the fluid from the wider pipe to the narrow throat of the venturimeter.

Explanation: When a venturimeter is placed in an inclined position, it continues to record the same reading. Its design allows it to accurately measure the flow rate of fluids regardless of the orientation of the pipe.

Explanation: The rate of flow through a venturimeter varies proportionally with the square root of the pressure difference between the inlet and the throat. This is directly related to the square root of the height of the liquid in the inlet.

Explanation: Mouthpieces are specifically employed to measure the rate of flow of fluids. They are commonly utilized in various fluid dynamics applications for accurate flow rate measurements.

Explanation: An orifice is termed a large orifice when the water head is five times the diameter of the pipe. This designation is essential in fluid mechanics when considering the impact of different orifice sizes on the flow dynamics.

Explanation: A triangular orifice is commonly used for low discharge applications. Its design allows for precise flow rate measurements, particularly in situations where the flow rates are relatively small.

Explanation: The orifice meter experiences the minimum head loss among the listed options. Its design enables efficient fluid flow with minimal energy losses, making it a preferred choice for certain flow measurement applications.

Explanation: The vena contracta is the section of the jet leaving an orifice that has the minimum cross-sectional area. Understanding this concept is crucial in fluid mechanics and flow rate calculations.

Explanation: At the vena contracta, the jet has the minimum cross-sectional area, resulting in the maximum velocity of the liquid at this specific section.

Explanation: A fluid particle is capable of various displacements, including translation, rotation, and distortion. Understanding these movements is crucial in analyzing fluid behavior and characteristics.

Explanation: For a long pipe, the head loss at the entrance and the outlet is typically neglected for simplification purposes in certain fluid flow calculations.

Explanation: In the case of laminar flow through a circular pipe, the maximum velocity is generally around 2.0 times the average velocity, representing a key characteristic of the flow behavior.

Explanation: When pipes are connected in series, the total rate of flow remains the same as that of flowing through each individual pipe. Understanding this principle is important in the analysis of fluid flow systems.

Explanation: When a fluid is at rest, the shear stress is zero. Shear stress in a fluid typically occurs when there is a velocity gradient within the fluid, leading to internal friction and deformation.

Explanation: A siphon is commonly employed to connect water reservoirs situated at different elevations, particularly when there is a natural or artificial obstruction, such as a hill, between them.

Explanation: A siphon is characterized by its inverted U-shape, allowing it to facilitate the movement of liquid from a higher elevation to a lower one without the need for external pumping mechanisms.

Explanation: To prevent any interruption in the flow of a siphon, an air vessel is typically provided at the summit. This design ensures the continuous movement of liquid through the siphon without any blockages or disruptions.

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Explanation: Not available

Explanation: The hydraulic radius in fluid mechanics is defined as the ratio of the cross-sectional area of flow to the wetted perimeter. It is a crucial parameter used in various hydraulic calculations and analyses.

Explanation: The wetted perimeter of a channel can be determined using the formula 4.75 times the square root of the flow rate (Q). Understanding this value is essential for assessing the characteristics of fluid flow in open channels.

Explanation: Manning’s formula finds application in the calculation of head loss due to friction in open channels. It is an essential tool in fluid dynamics for determining the impact of friction on the energy of flowing fluids.

Explanation: Manning’s formula for flow in open channels is represented by the equation v = 1/n R^2/3 S^1/2, where v is the average velocity, n is the Manning’s roughness coefficient, R is the hydraulic radius, and S is the channel slope.

Explanation: The Darcy-Weisbach equation is commonly used to calculate head loss due to friction in a pipe. It considers factors such as the pipe length (L), flow velocity (V), friction factor (f), and the acceleration due to gravity (g).

Explanation: Head loss in a pipe is directly influenced by the flow velocity. As the velocity increases, the head loss also increases, indicating a higher energy dissipation due to friction within the pipe.

Explanation: Chazy’s formula is utilized for determining the velocity of flow in channels. It provides a means of assessing the flow characteristics and behavior of fluids in open channels.

Explanation: Chazy’s formula is represented by the equation v = C√mi, where v is the velocity of flow, C is a constant, m is the hydraulic mean depth, and i is the hydraulic gradient of the channel.

Explanation: When a liquid jet is released from a nozzle exposed to the atmosphere, it typically follows a parabolic path. This behavior is influenced by factors such as gravitational force and initial velocity.

Explanation: The floating method is not specifically used for the measurement of discharge, head, or pressure. It may refer to various techniques or principles that involve buoyancy and fluid mechanics but is not exclusively tied to any specific measurement method.

Explanation: The float method is commonly utilized to measure the velocity of flow in an open channel. By tracking the movement of a float on the surface of the flowing fluid, the velocity can be accurately determined.

Explanation: A pitot tube is a device specifically used to measure the velocity of flow in a fluid. It operates based on the principle of converting the kinetic energy of the fluid into measurable pressure differences, enabling the determination of flow velocity.

Explanation: When a pitot tube is oriented with its nose facing downstream, the liquid inside the tube falls to a depth equivalent to the square root of the velocity squared divided by twice the acceleration due to gravity (v^2/2g).

Explanation: When a pitot tube is positioned with its nose facing sideways, the liquid within the tube neither rises nor falls. The lack of vertical orientation prevents the liquid from exhibiting any significant movement in the tube.

Explanation: The actual velocity through an orifice is typically less than the theoretical velocity. This reduction is primarily attributed to various factors, including frictional losses and the effects of the vena contracta, leading to a decrease in the flow velocity.

Explanation: The most economical section of a circular channel for achieving the maximum discharge involves specific relationships among the depth of water, hydraulic mean depth, and wetted perimeter relative to the diameter of the circular section.

Explanation: The most economical section of a circular channel for obtaining the maximum velocity is determined based on the relationship between the depth of water, hydraulic mean depth, and wetted perimeter in relation to the diameter of the circular section.

Explanation: The condition for achieving the maximum velocity and discharge in closed flow scenarios involves specific ratios relative to the diameter (D) of the system. These relationships are crucial in optimizing the flow characteristics for maximum efficiency.

Explanation: The trapezoidal channel section is regarded as one of the most efficient configurations for fluid flow, offering optimal balance and performance in various hydraulic applications. Its design facilitates effective flow characteristics and efficient conveyance of fluids.

Explanation: An error of 1% in measuring H typically leads to a 1.5% variation in the results. It is important to consider potential errors and inaccuracies in measurements to ensure the accuracy of calculations and analysis in fluid mechanics.

Explanation: The rise of the water table resulting from the transition of super-critical flow to stable streaming can be identified as a hydraulic jump or a standing wave. This phenomenon involves changes in the flow characteristics and dynamics within the channel.

Explanation: The maximum discharge through a trapezoidal channel is achieved when the specific ratio ‘m’ is equal to half the depth ‘d’. This condition indicates an optimal configuration for maximizing the flow rate through the channel.

Explanation: The discharge through a rectangular channel is maximized when the specific ratio ‘m’ is equal to half the depth ‘d’ or when the depth ‘d’ is equal to half the breadth ‘b’. These conditions signify an optimal configuration for achieving maximum flow rate.

Explanation: The maximum discharge through a trapezoidal channel occurs when half of the width of the channel is equal to the length of the sloping side. This configuration facilitates optimal flow characteristics within the channel.

Explanation: Alternate depths refer to the two specific depths in a channel at which the same discharge can be observed for the identical specific force. Understanding these alternate depths is essential for analyzing the behavior of fluid flow within the channel.

Explanation: The specific energy in a channel section typically increases when the depth of super critical flow decreases. This behavior is influenced by various factors related to the flow dynamics and energy characteristics within the channel.

Explanation: A hydraulic jump is a phenomenon that occurs in open channels, involving a sudden transition from a high-velocity flow to a low-velocity flow. This results in a noticeable rise in the liquid surface within the channel.

Explanation: The depth of flow after the hydraulic jump is determined using the formula d2 = d1/2 [√1+8(Fe)1^2 -1]. This equation accounts for the change in depth as a result of the hydraulic jump phenomenon within the channel.

Explanation: The depth of flow at which the specific energy is at its minimum is referred to as the critical depth. This specific depth value plays a critical role in the analysis of flow characteristics and energy dynamics within the channel.

Explanation: The critical depth (he) is calculated using the equation (q^2/g)^1/3, where q represents the rate of flow per unit width of the channel. This critical depth value is significant in understanding the characteristics of flow in open channels.

Explanation: Super-critical flow is typically observed in channels with steep slopes. This flow condition involves a higher flow velocity and a specific Froude number range, signifying rapid and turbulent flow dynamics within the channel.

Explanation: The wetted perimeter for a circular channel can be calculated using the formula 2Rθ, where θ represents half the angle subtended by the water at the center and R denotes the radius of the circular channel. This equation helps determine the total perimeter in contact with the flowing water.

Explanation: Water hammer is a hydraulic phenomenon that arises as a result of the sudden increase in pressure due to the abrupt closure of a valve in a pipeline system. Understanding the implications of water hammer is essential in designing and maintaining effective fluid transport systems.

Explanation: The magnitude of water hammer is influenced significantly by the length of the pipeline. Other factors, such as the elastic properties of the liquid and pipe material, also play a role, but the length of the pipeline is particularly crucial in determining the severity of the water hammer effect.

Explanation: The hydraulic ram operates based on the principle of water hammer. This mechanism involves the conversion of the kinetic energy of flowing water into pressure energy, allowing for the pumping of water to higher elevations without the need for external power sources.

Explanation: The hydraulic ram is specifically designed to lift water to higher elevations without the use of an electric motor. It utilizes the energy generated by the water hammer effect to pump water against gravity, making it a valuable device in various hydraulic applications.

Explanation: Open channel flow refers to the type of flow in which the liquid is conveyed through a conduit with a free surface. This configuration allows for the observation of the liquid surface and the interaction of the flowing fluid with the surrounding environment.

Explanation: In open channel flow, the flow of the liquid occurs at the expense of hydraulic pressure. This dynamic is a critical aspect of understanding the energy characteristics and behavior of the flowing liquid within the channel.

Explanation: In open channel flow, the hydraulic gradient line typically lies above the liquid surface. This relationship reflects the energy distribution and characteristics within the flow, indicating the specific pressures and forces acting on the flowing liquid.

Explanation: In uniform flow in a channel, the total energy line, hydraulic gradient line, and the bottom of the channel are parallel to each other. This alignment indicates a stable flow condition within the channel.

Explanation: In an open channel, the maximum velocity occurs slightly below the free surface of the flow. This phenomenon is due to the velocity distribution within the channel and can be observed at a depth below the free surface.

Explanation: The ratio of the mean velocity to the surface velocity in open channels is approximately 0.88. This ratio is relevant for understanding the velocity distribution and characteristics in open channel flow.

Explanation: Not available.

Explanation: In the case of vortex flow, the level of water at the center is lower than the circumference. Vortex flow is characterized by swirling motion, and the central region typically has lower water levels.

Explanation: The water immediately downstream of a conduit or weir in an open channel is referred to as “tail water.” It plays a significant role in hydraulic calculations and channel flow analysis.

Explanation: The upward water pressure at the base of a structure is often referred to as “uplist.” This term is used in hydraulic engineering to describe the pressure exerted by the flowing water on the base of the structure.

Explanation: Rotation in fluid dynamics is defined as the movement of a fluid element in such a way that both of its axes rotate in the same direction. This characteristic is associated with rotational flow patterns in fluids.

Explanation: An intensifier is a device used to increase pressure, often in the context of hydraulic systems. It helps amplify the pressure of a fluid for various applications, such as fluid power systems and industrial processes.

Explanation: Afflux is defined as the maximum increase in water level in the path of the flow of water, particularly in open channels or rivers. It is a critical factor in flood modeling and river engineering.

Explanation: The profile of rising water on the upstream side of a dam is known as the “back water curve.” This curve describes the elevation of the water surface upstream of the dam and is a vital consideration in dam design and analysis.

Explanation: A back water curve is typically caused when there is an obstruction in the channel, such as a weir or dam. This obstruction leads to changes in the water surface profile upstream of the structure.

Explanation: The numerical value of vorticity in fluid dynamics is typically twice that of the rotational velocity. Vorticity is an important parameter in understanding fluid rotation and flow patterns.

Explanation: Cavitation in flowing fluid occurs when the total energy of the fluid suddenly decreases. This can lead to the formation of vapor bubbles and other undesirable effects in hydraulic systems.

Explanation: Cavitation is primarily caused by low pressures in flowing fluids, leading to the formation of vapor bubbles or cavities. It can have detrimental effects on the hydraulic system and the surfaces exposed to cavitation.

Explanation: Cavitation is typically collapsed by high pressures in the fluid. Applying higher pressures helps eliminate the vapor bubbles or cavities formed during the cavitation process.

Explanation: A water cushion is often used to dissipate or destroy the excess energy in hydraulic systems. It helps regulate and stabilize the flow of water, preventing sudden pressure fluctuations and undesirable effects in the system.

Explanation: The dimensionless number can be conveniently represented as WIS-MIE-RIV-FIG-EIP for easy recollection and identification. This representation helps in better understanding and application of various dimensionless parameters in fluid dynamics and engineering.

Explanation: Reynolds number is the ratio of the initial force, often inertia, to the viscosity of the fluid. It is a dimensionless quantity used to predict flow patterns in different fluid flow scenarios, indicating whether the flow is laminar or turbulent.

Explanation: In pipe flow, the flow is considered turbulent if the Reynolds number exceeds 3000. This indicates that the flow is highly turbulent and characterized by chaotic and irregular fluid motion within the pipe.

Explanation: When a liquid flows from an open-ended tube (nozzle) and forms a spray of liquid drops, the relevant dimensionless number is the Weber number. The Weber number describes the balance between inertia and surface tension forces.

Explanation: The Froude number is the ratio of the inertia and gravitational forces in any flow, particularly when other forces can be ignored. It is used to classify the flow regime in open channels and flumes.

Explanation: The Mach number is the ratio of inertia force to elasticity (or compressibility) in fluid dynamics. It is commonly used in aerodynamics to determine the flow regime of gases, particularly in supersonic or subsonic flows.

Explanation: The Weber number is the ratio of inertia force to surface tension in fluid dynamics. It is used to assess the importance of surface tension in various flow situations, such as droplet formation.

Explanation: When inertia and gravitational forces are dominant in the flow, and frictional resistance is relatively minor, the design of channels is typically based on comparing the Froude number. This is especially relevant for open channel flow design.

Explanation: Euler’s number is the ratio of inertia force to pressure force. It is used to characterize the compressibility effects in fluid dynamics, particularly in the context of aerodynamics.

Explanation: Among the given options, the Mach number is dimensionless. The Mach number characterizes the speed of an object (often an aircraft) relative to the speed of sound and is a dimensionless parameter used in fluid dynamics.

Explanation: The power transmitted through a pipe can be calculated using the formula WxQx(H-h_f)/75, where W represents weight, Q is the flow rate, H is the total head, and h_f is the head loss.

Explanation: One horsepower (HP) is approximately equal to 0.746 kilowatts (kW). This conversion factor is commonly used to relate power measurements in different units.

Explanation: If the total head is 37.5 meters and the discharge is 1 cubic meter per second, the power generated can be calculated, and it is approximately 500 horsepower (HP).

Explanation: The upper surface of a weir over which water flows is known as the “crest” of the weir.

Explanation: A surface float is used to measure the viscosity of flow in a fluid, particularly in industrial and laboratory applications.

Explanation: The pressure within a soap bubble is greater than the external pressure. This pressure differential is what keeps the bubble stable and maintains its shape.

Explanation: The maximum efficiency of power transmission through a pipe is typically around 66%. This represents the highest level of power transfer efficiency achievable in hydraulic systems.

Explanation: The hydrostatic pressure on a dam depends on both its depth and shape. The depth of the water reservoir behind the dam and the shape of the dam play a significant role in determining the pressure exerted on the dam structure.

Explanation: When pipes are connected in parallel, the total loss of head in the system is the same as the loss of head in each individual pipe. This is a key principle in fluid flow analysis.

Explanation: The velocity of flow can be determined by dividing the discharge by the area of flow. This relationship helps to establish the speed of fluid movement within a specific channel or conduit.

Explanation: The discharge through a V-notch weir is directly proportional to the angle of the V-notch and the depth of the flow. This relationship governs the flow characteristics over the V-notch weir structure.

Explanation: In the case of a broad-crested weir, the depth of water h at the end of the still is approximately equal to the total head H. This relationship is crucial in determining the behavior of flow over the weir.

Explanation: The discharge over a rectangular notch is directly proportional to the square root of the head (H) raised to the power of 3/2. This relationship helps in the calculation and analysis of fluid flow characteristics over the rectangular notch.

Explanation: Steady flow refers to a situation in fluid dynamics where the fluid or flow parameters remain constant at every point in space at any given instant. It implies that the flow does not change with time at any specific point.

Explanation: A submerged weir is a type of weir where the water level on the downstream side is higher than the top surface of the weir. This can lead to unique flow characteristics and considerations in hydraulic engineering.

Explanation: In a long pipe, the basic head loss primarily occurs due to friction between the fluid and the pipe walls. This frictional head loss is a result of the viscosity of the fluid and the roughness of the pipe surface.

Explanation: Borda’s mouthpiece running full typically has the highest coefficient of discharge among the given options. The coefficient of discharge is a measure of the efficiency of a particular flow measurement device.

Explanation: The hydrostatic force exerted by water is proportional to the depth and other parameters. In this case, with a 2 m deep water level, the force exerted on the gate downstream is equal to 20 kN.

Explanation: The total energy of a liquid in motion includes the pressure energy, kinetic energy, and potential energy. These components collectively contribute to the energy of the fluid system.

Explanation: The property described in this question is that of steady flow. In steady flow, the fluid properties remain constant at any given point in space over time.

Explanation: Piezometers are used to measure very low pressures. They are commonly employed in geotechnical and hydraulic engineering applications.

Explanation: The upper surface of the weir over which water flows is known as the “nappe” of the weir. It is the sheet of water that flows over the crest of the weir.

Explanation: The quantity of mass of a fluid is not affected by the acceleration due to gravity, the distance from the center of the earth, or the elevation of the body. These factors primarily influence the weight of the fluid.

Explanation: The magnitude of capillary rise is generally higher in clays compared to other types of soil such as silts, sands, or gravels. This is due to the finer particles and the higher capillary action in clay soils.

Explanation: The total pressure force on a plane area is equal to the product of the area and the intensity of pressure at its centroid for any orientation, whether the area is horizontal, vertical, or inclined.

Explanation: The viscosity of a liquid typically decreases with increasing temperature. This phenomenon is common in many liquids and is an essential consideration in various fluid dynamics applications.

Explanation: Viscosity describes the internal friction of a moving fluid. It is a measure of the resistance to deformation in a fluid due to internal frictional forces.

Explanation: Bernoulli’s equation is a fundamental principle in fluid dynamics that relates the velocity, pressure, and elevation in a fluid flow system. It can be applied to various flow measurement devices such as venturimeters, orifice meters, and pitot tubes.

Explanation: The rate of flow through a V-notch varies as the fifth power of the depth (H). This relationship is critical in understanding the flow characteristics over V-notch weirs and similar flow control structures.

Explanation: Specific gravity is the ratio of the density of a substance to the density of a reference substance. It is a dimensionless quantity often used in fluid mechanics and related fields.

Explanation: Orifice meters are commonly used to measure the discharge of fluids. They work based on the principle of fluid flow through an orifice, providing valuable information about the flow rate of the fluid.