**Correct Answer: total loss due to friction / total length of the channel**

**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.

**Correct Answer: all of the above**

**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.

**Correct Answer: (v^2/2g) + h**

**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.

**Correct Answer: conjugate depths**

**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.

_{a}) is given by

_{a}= Discharge over notch / Area of notch

_{a}= Discharge over notch / Area of channel

_{a}= Discharge over notch / Head over notch x width of channel

**Correct Answer: V _{a}= Discharge over notch / Area of channel**

**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.

_{v}, C

_{c}and C

_{d}are the hydraulic coefficients of an orifice, then

_{d}= C

_{c}.C

_{v}

_{r}= 1+C

_{v}^2/C

_{d}

_{v}= C

_{c}+ C

_{d}

_{c}= C

_{v}/C

_{d}

**Correct Answer: C _{d} = C_{c}.C_{v}**

**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.

**Correct Answer: less than the width of the channel**

**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.

**Correct Answer: sill**

**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.

**Correct Answer: submerged weir**

**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.

**Correct Answer: H:V::1:4**

**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.

_{d}√

_{2g}LH

^{3/2}

_{d}LH√(2gH)

_{d}H√(2gL^2H)

**Correct Answer: all of the above**

**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.

_{d}L√(2g)H

^{3/2}

_{d}B√(2g)H

^{3/2}

_{d}L√(2g)H

^{3/2}

_{d}B√(2g)H

^{3/2}

**Correct Answer: Q=2/3 C _{d}B√(2g)H^{3/2}**

**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.

**Correct Answer: 2.73 m**

**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.

_{a}is

**Correct Answer: Q/L(H+L)**

**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.

**Correct Answer: 25% to 30%**

**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.

^{5/2}Tan0/2

^{3/2}Tan0/2

^{1/2}Tan0/2

**Correct Answer: 8/15 Cd√2gH ^{5/2}Tan0/2**

**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.

**Correct Answer: 90°**

**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.

**Correct Answer: it gives more accurate results for low discharge (Q≤100m^3/sec)**

**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.

^{3/2}

^{3/2}

^{3/2}

^{3/2}

**Correct Answer: 2/3 CdL√2gH ^{3/2}**

**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.

^{3/2}

^{5/2}

**Correct Answer: H ^{5/2}**

**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.

**Correct Answer: rectangular notches of different sizes**

**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.

**Correct Answer: 3/2**

**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.

**Correct Answer: 5/2**

**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.

**Correct Answer: 0.1H**

**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.

_{d}= 0.035 is

**Correct Answer: 0.0160 cm³/sec**

**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.

**Correct Answer: trapezoidal weir, whose sides slope 1 horizontal to 4 verticals**

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

**Correct Answer: one-half of the height of water on the sill**

**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.

**Correct Answer: Cipolleti weir**

**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.

**Correct Answer: all of the above**

**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.

**Correct Answer: discharge of fluids**

**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.

**Correct Answer: rate of flow**

**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.

**Correct Answer: equal to the convergent cone**

**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.

**Correct Answer: is less than the outlet length**

**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.

**Correct Answer: same reading**

**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.

**Correct Answer: H^1/2**

**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.

**Correct Answer: rate of flow**

**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.

**Correct Answer: five times the diameter of the pipe**

**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.

**Correct Answer: triangular**

**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.

**Correct Answer: orifice meter**

**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.

**Correct Answer: vena contracta**

**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.

**Correct Answer: maximum**

**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.

**Correct Answer: all of the above**

**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.

**Correct Answer: at the entrance and outlet both are ignored**

**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.

**Correct Answer: the maximum velocity=2.0 times the average velocity**

**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.

**Correct Answer: is the same as flowing through each pipe**

**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.

**Correct Answer: zero**

**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.

**Correct Answer: to connect water reservoirs at different levels intervened by a hill**

**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.

**Correct Answer: inverted U-shaped pipe**

**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.

**Correct Answer: at the summit**

**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.

^{4}[l

_{1}/d

_{1}^4 + l

_{2}/d

_{2}^4 + l

_{3}/d

_{3}^4 + …..]

^{3}[l

_{1}/d

_{1}^3 + l

_{2}/d

_{2}^3 + l

_{3}/d

_{3}^3 + …..]

^{5}[l

_{1}/d

_{1}^5 + l

_{2}/d

_{2}^5 + l

_{3}/d

_{3}^5 + …..]

^{2}[l

_{1}/d

_{1}^2 + l

_{2}/d

_{2}^2 + l

_{3}/d

_{3}^2 + …..]

**Correct Answer: L = D ^{5}[l_{1}/d_{1}^5 + l_{2}/d_{2}^5 + l_{3}/d_{3}^5 + …..]**

**Explanation:** Not available

^{2/5}

^{1/5}

^{3/5}

^{4/5}

**Correct Answer: d = D/n ^{2/5}**

**Explanation:** Not available

**Correct Answer: wetted area divided by the wetted perimeter**

**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.

**Correct Answer: 4.75√Q**

**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.

**Correct Answer: head loss due to friction 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.

**Correct Answer: v = 1/n R^2/3 S^1/2**

**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.

**Correct Answer: h_f = fLV^2/2gd**

**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).

**Correct Answer: an increase in velocity**

**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.

**Correct Answer: velocity of flow in channels**

**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.

**Correct Answer: v = C√mi**

**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.

**Correct Answer: a parabolic path**

**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.

**Correct Answer: none of the above**

**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.

**Correct Answer: the velocity in an open channel**

**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.

**Correct Answer: velocity of flow**

**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.

**Correct Answer: falls in the tube to a depth √v^2/2g**

**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).

**Correct Answer: neither rises nor falls in the tube**

**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.

**Correct Answer: less**

**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.

**Correct Answer: all of the above**

**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.

**Correct Answer: all of the above**

**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.

**Correct Answer: 0.81D & 0.95D**

**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.

**Correct Answer: trapezoidal**

**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.

**Correct Answer: 1.5%**

**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.

**Correct Answer: both (a) and (b) above**

**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.

**Correct Answer: m = d/2**

**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.

**Correct Answer: both (a) and (b) above**

**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.

**Correct Answer: half of the width = sloping side**

**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.

**Correct Answer: alternate depths**

**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.

**Correct Answer: decreases in depth of super critical flow**

**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.

**Correct Answer: hydraulic jump**

**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.

**Correct Answer: d2 = d1/2 [√1+8(Fe)1^2 -1]**

**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.

**Correct Answer: critical depth**

**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.

**Correct Answer: (q^2/g)^1/3**

**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.

**Correct Answer: steep slope**

**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.

**Correct Answer: 2Rθ**

**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.

**Correct Answer: when pressure increases sudden closure of the valve**

**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.

**Correct Answer: the length of the pipeline**

**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.

**Correct Answer: the principle of water hammer**

**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.

**Correct Answer: for lifting water without an electric motor**

**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.

**Correct Answer: one in which the liquid is flowing in a conduit and has a free surface**

**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.

**Correct Answer: the flow takes place at the expense of hydraulic pressure**

**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.

**Correct Answer: the hydraulic gradient line is higher than the liquid surface**

**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.

**Correct Answer: the total energy line, hydraulic gradient line, and the bottom of the channel are parallel**

**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.

**Correct Answer: slightly below the free surface**

**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.

**Correct Answer: 0.88**

**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.

**Correct Answer: energy equation**

**Explanation:** Not available.

**Correct Answer: lower than circumference**

**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.

**Correct Answer: tail water**

**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.

**Correct Answer: uplist**

**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.

**Correct Answer: the same direction**

**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.

**Correct Answer: pressure**

**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.

**Correct Answer: afflux**

**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.

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