Questions and Answers of Fluid Mechanics

Water is to be transported in a clay tile lined rectangular channel at a rate of 0.8 m3/s. The channel bottom slope is 0.0015. The width of the channel for the best cross section is(a) 0.68 m (b)
Water is to be transported in a clay tile lined trapezoidal channel at a rate of 0.8 m3/s. The channel bottom slope is 0.0015. The width of the channel for the best cross section is(a) 0.48 m(b) 0.70
Water flows uniformly in a finished-concrete rectangular channel with a bottom width of 0.85 m. The flow depth is 0.4 m and the bottom slope is 0.003. The channel should be classified as(a)
Water discharges into a rectangular horizontal channel from a sluice gate and undergoes a hydraulic jump. The channel is 25-m-wide and the flow depth and velocity before the jump are 2 m and 9 m/s,
Water discharges into a rectangular horizontal channel from a sluice gate and undergoes a hydraulic jump. The flow depth and velocity before the jump are 1.25 m and 6 m/s, respectively. The
Water discharges into a 7-m-wide rectangular horizontal channel from a sluice gate and undergoes a hydraulic jump. The flow depth and velocity before the jump are 0.65 m and 5 m/s, respectively. The
Water is released from a 0.8-m-deep reservoir into a 4-m-wide open channel through a sluice gate with a 0.1-m-high opening at the channel bottom. The flow depth after all turbulence subsides is 0.5
The flow rate of water in a 3-m-wide horizontal open channel is being measured with a 0.4-m-high sharp-crested rectangular weir of equal width. If the water depth upstream is 0.9 m, the flow rate of
Using catalogs or websites, obtain information from three different weir manufacturers. Compare the different weir designs, and discuss the advantages and disadvantages of each design. Indicate the
Reconsider Prob. 13–53. If the maximum flow height the channel can accommodate is 3.2 m, determine the maximum flow rate through the channel.Data from Problem 13–53A trapezoidal channel with a
Consider water flow in the range of 10 to 15 m3/s through a horizontal section of a 5-m-wide rectangular channel. A rectangular or triangular thin-plate weir is to be installed to measure the flow
Consider water flow through two identical channels with square flow sections of 4 m × 4 m. Now the two channels are combined, forming a 8-m-wide channel. The flow rate is adjusted so that the flow
A cast iron V-shaped water channel shown in Fig. P13–56 has a bottom slope of 0.5°. For a flow depth of 0.75 m at the center, determine the discharge rate in uniform flow.FIGURE P13–56
Water is to be transported in a cast iron rectangular channel with a bottom width of 6 ft at a rate of 70 ft3/s. The terrain is such that the channel bottom drops 1.5 ft per 1000 ft length. Determine
A clean-earth trapezoidal channel with a bottom width of 1.8 m and a side surface slope of 1:1 is to drain water uniformly at a rate of 8 m3/s to a distance of 1 km. If the flow depth is not to
Water flows in a channel whose bottom slope is 0.002 and whose cross section is as shown in Fig. P13–60. The dimensions and the Manning coefficients for the surfaces of different subsections are
A water draining system with a constant slope of 0.0025 is to be built of three circular channels made of finished concrete. Two of the channels have a diameter of 1.8 m and drain into the third
A 2-m-internal-diameter circular steel storm drain (n = 0.012) is to discharge water uniformly at a rate of 12 m3/s to a distance of 1 km. If the maximum depth is to be 1.5 m, determine the required
Water is to be transported at a rate of 10 m3/s in uniform flow in an open channel whose surfaces are asphalt lined. The bottom slope is 0.0015. Determine the dimensions of the best cross section if
Consider uniform flow in an asphalt-lined rectangular channel with a flow area of 2 m2 and a bottom slope of 0.0003. By varying the depth-to-width ratio y/b from 0.1 to 2.0, calculate and plot the
A trapezoidal channel made of unfinished concrete has a bottom slope of 1°, base width of 5 m, and a side surface slope of 1:1, as shown in Fig. P13–55. For a flow rate of 25 m3/s, determine the
A rectangular channel with a bottom slope of 0.0004 is to be built to transport water at a rate of 750 ft3/s. Determine the best dimensions of the channel if it is to be made of (a) Unfinished
Repeat Prob. 13–64E for a flow rate of 650 ft3/s.Data from Problem 13–64EA rectangular channel with a bottom slope of 0.0004 is to be built to transport water at a rate of 750 ft3/s. Determine
Consider steady flow of water in a horizontal channel of rectangular cross section. If the flow is subcritical, the flow depth will (a) Increase, (b) Remain constant, (c) Decrease in the flow
Why is the hydraulic jump sometimes used to dissipate mechanical energy? How is the energy dissipation ratio for a hydraulic jump defined?
Is it possible for subcritical flow to undergo a -hydraulic jump? Explain.
Consider steady flow of water in an upward-sloped channel of rectangular cross section. If the flow is supercritical, the flow depth will (a) Increase, (b) Remain constant,(c) Decrease in the flow
Someone claims that frictional losses associated with wall shear on surfaces can be neglected in the analysis of rapidly varied flow, but should be considered in the analysis of gradually varied
How does nonuniform or varied flow differ from uniform flow?
How does gradually varied flow (GVF) differ from rapidly varied flow (RVF)?
Repeat Prob. 13–66 for a weedy excavated earth channel with n = 0.030.Data from Problem 66A trapezoidal channel made of unfinished concrete has a bottom slope of 1°, base width of 5 m, and a side
For sluice gates, how is the discharge coefficient Cd defined? What are typical values of Cd for sluice gates with free outflow? What is the value of Cd for the idealized frictionless flow through
What is the basic principle of operation of a broad-crested weir used to measure flow rate through an open channel?
Consider gradually varied flow of water in a wide rectangular irrigation channel with a per-unit- width flow rate of 5m3/s·m, a slope of 0.01, and a Manning coefficient of 0.02. The flow is
What is a sharp-crested weir? On what basis are the sharp-crested weirs classified?
Consider gradually varied flow of water in a 20-ft wide rectangular channel with a flow rate of 300 ft3/s and a Manning coefficient of 0.008. The slope of the channel is 0.01, and at the location x =
Consider the gradually varied flow equation,For the case of a wide rectangular channel, show that this can be reduced to the following form, which explicitly shows the importance of the relationship
While the GVF equation cannot be used to predict a hydraulic jump directly, it can be coupled with the ideal hydraulic jump depth ratio equation in order to help locate the position at which a jump
Repeat Problem 13–90 for the case of an initial water depth of 0.75 m instead of 1.25 m.Data from Problem 13–90Consider a wide rectangular water channel with a per-unit-width flow rate of
Consider gradually varied flow over a bump in a wide channel, as shown in Fig. P13–89. FIGURE P13–89The initial flow velocity is 0.75 m/s, the initial flow depth is 1 m, the Manning parameter is
Consider a wide rectangular water channel with a per-unit-width flow rate of 5m3/s·m and a Manning coefficient of n = 0.02. The channel is comprised of a 100 m length having a slope of S01 = 0.01
During a hydraulic jump in a wide channel, the flow depth increases from 0.6 to 3 m. Determine the velocities and Froude numbers before and after the jump, and the energy dissipation ratio.
Consider uniform flow of water in a wide rectangular channel with a per-unit-width flow rate of 1.5 m3/s·m and a Manning coefficient of 0.03. The slope of the channel is 0.0005. (a) Calculate the
Water flowing in a wide horizontal channel at a flow depth of 56 cm and an average velocity of 9 m/s undergoes a hydraulic jump. Determine the head loss associated with the hydraulic jump.
Water flowing in a wide channel at a depth of 2 ft and a velocity of 40 ft/s undergoes a hydraulic jump. Determine the flow depth, velocity, and Froude number after the jump, and the head loss
The flow depth and velocity of water after undergoing a hydraulic jump are measured to be 1.1 m and 1.75 m/s, respectively. Determine the flow depth and velocity before the jump, and the fraction of
Water discharging into an 8-m-wide rectangular horizontal channel from a sluice gate is observed to have undergone a hydraulic jump. The flow depth and velocity before the jump are 1.2 m and 9 m/s,
Consider the flow of water in a 10-m-wide channel at a rate of 70 m3/s and a flow depth of 0.50 m. The water now undergoes a hydraulic jump, and the flow depth after the jump is measured to be 4 m.
Water flows uniformly in a rectangular channel with finished-concrete surfaces. The channel width is 3 m, the flow depth is 1.2 m, and the bottom slope is 0.002. Determine if the channel should be
Consider the flow of water through a 12-ft-wide unfinished-concrete rectangular channel with a bottom slope of 0.5°. If the flow rate is 300 ft3/s, determine if the slope of this channel is mild,
Consider uniform water flow in a wide brick channel of slope 0.48. Determine the range of flow depth for which the channel is classified as being steep.
Water is flowing in a 90° V-shaped cast iron channel with a bottom slope of 0.002 at a rate of 3 m3/s. Determine if the slope of this channel should be classified as mild, critical, or steep for
Consider steady flow of water in a downward sloped channel of rectangular cross section. If the flow is subcritical and the flow depth is less than the normal depth (y < yn), the flow depth will (a)
Consider steady flow of water in a horizontal channel of rectangular cross section. If the flow is supercritical, the flow depth will (a) Increase, (b) Remain constant, (c) Decrease in the flow
Consider steady flow of water in a downward sloped channel of rectangular cross section. If the flow is subcritical and the flow depth is greater than the normal depth (y > yn), the flow depth
Consider uniform water flow in a wide rectangular channel with a depth of 2 m made of unfinished concrete laid on a slope of 0.0022. Determine the flow rate of water per m width of channel. Now water
Draw a flow depth-specific energy diagram for flow through underwater gates, and indicate the flow through the gate for cases of (a) Frictionless gate, (b) Sluice gate with free outflow, (c)
Consider the flow of a liquid over a bump during subcritical flow in an open channel. The specific energy and the flow depth decrease over the bump as the bump height is increased. What will the
Consider steady frictionless flow over a bump of height Δz in a horizontal channel of constant width b. Will the flow depth y increase, decrease, or remain constant as the fluid flows over the bump?
Water flowing in a wide channel encounters a 22-cm-high bump at the bottom of the channel. If the flow depth is 1.2 m and the velocity is 2.5 m/s before the bump, determine if the flow is choked over
Consider the uniform flow of water in a wide channel with a velocity of 8 m/s and flow depth of 0.8 m. Now water flows over a 30-cm-high bump. Determine the change (increase or decrease) in the water
Water is released from a 12-m-deep reservoir into a 6-m-wide open channel through a sluice gate with a 1-m-high opening at the channel bottom. If the flow depth downstream from the gate is measured
A full-width sharp-crested weir is to be used to measure the flow rate of water in a 7-ft-wide rectangular channel. The maximum flow rate through the channel is 180 ft3/s, and the flow depth upstream
The flow rate of water in a 10-m-wide horizontal channel is being measured using a 1.3-m-high sharp-crested rectangular weir that spans across the channel. If the water depth upstream is 3.4 m,
Repeat Prob. 13–107 for the case of a weir height of 1.6 m.Data from Prob. 13–107.The flow rate of water in a 10-m-wide horizontal channel is being measured using a 1.3-m-high sharp-crested
Water flows over a 2-m-high sharp-crested rectangular weir. The flow depth upstream of the weir is 3 m, and water is discharged from the weir into an unfinished-concrete channel of equal width where
Water flows through a sluice gate with a 1.1-fthigh opening and is discharged with free outflow. If the upstream flow depth is 5 ft, determine the flow rate per unit width and the Froude number
Repeat Prob. 13–110E for the case of a drowned gate with a downstream flow depth of 3.3 ft.Data from Problem 13–110EWater flows through a sluice gate with a 1.1-fthigh opening and is discharged
Water is to be discharged from an 8-m-deep lake into a channel through a sluice gate with a 5-m wide and 0.6-m-high opening at the bottom. If the flow depth downstream from the gate is measured to be
Consider water flow through a wide channel at a flow depth of 8 ft. Now water flows through a sluice gate with a 1-ft-high opening, and the freely discharged outflow subsequently undergoes a
The flow rate of water flowing in a 5-m-wide channel is to be measured with a sharp-crested triangular weir 0.5 m above the channel bottom with a notch angle of 80°. If the flow depth upstream from
Repeat Prob. 13–114 for an upstream flow depth of 0.90 m.Data from Problem 13-114The flow rate of water flowing in a 5-m-wide channel is to be measured with a sharp-crested triangular weir 0.5 m
A sharp-crested triangular weir with a notch angle of 100° is used to measure the discharge rate of water from a large lake into a spillway. If a weir with half the notch angle (θ = 50°) is used
A 0.80-m-high broad-crested weir is used to measure the flow rate of water in a 5-m-wide rectangular channel. The flow depth well upstream from the weir is 1.8 m. Determine the flow rate through the
Repeat Prob. 13–117 for an upstream flow depth of 1.4 m.Data from Problem 13–117 A 0.80-m-high broad-crested weir is used to measure the flow rate of water in a 5-m-wide rectangular channel. The
Consider uniform water flow in a wide channel made of unfinished concrete laid on a slope of 0.0022. Now water flows over a 15-cm-high bump. If the flow over the bump is exactly critical (Fr = 1),
Consider water flow over a 0.80-m-high sufficiently long broad-crested weir. If the minimum flow depth above the weir is measured to be 0.50 m, determine the flow rate per meter width of channel and
The flow rate of water through a 8-m-wide (into the paper) channel is controlled by a sluice gate. If the flow depths are measured to be 0.9 and 0.25 m upstream and downstream from the gates,
Water flows in a canal at an average velocity of 4 m/s. Determine if the flow is subcritical or supercritical for flow depths of (a) 0.2 m, (b) 2 m, (c) 1.63 m.
A trapezoidal channel with a bottom width of 4 m and a side slope of 45° discharges water at a rate of 18 m3/s. If the flow depth is 0.6 m, determine if the flow is subcritical or supercritical.
A 5-m-wide rectangular channel lined with finished concrete is to be designed to transport water to a distance of 1 km at a rate of 12 m3/s. Using EES (or other) software, investigate the effect of
Repeat Prob. 13–124 for a trapezoidal channel that has a base width of 5 m and a side surface angle of 45°.Data from Problem 124A 5-m-wide rectangular channel lined with finished concrete is to be
A trapezoidal channel with brick lining has a bottom slope of 0.001 and a base width of 4 m, and the side surfaces are angled 25° from the horizontal, as shown in Fig. P13–126. If the normal depth
Water flows through a 2.2-m-wide rectangular channel with a Manning coefficient of n = 0.012. If the water is 0.9 m deep and the bottom slope of the channel is 0.6°, determine the rate of discharge
Consider the flow of water through a parabolic notch shown in Fig. P13–131. Develop a relation for the flow rate, and calculate its numerical value for the ideal case in which the flow velocity is
Reconsider Prob. 13–129. By varying the flow depth-to-radius ratio y/R from 0.1 to 1.9 while holding the flow area constant and evaluating the flow rate, show that the best cross section for flow
Consider a 1-m-internal-diameter water channel made of finished concrete (n = 0.012). The channel slope is 0.002. For a flow depth of 0.32 m at the center, determine the flow rate of water through
A rectangular channel with a bottom width of 7 m discharges water at a rate of 45 m3/s. Determine the flow depth below which the flow is supercritical.
Water flows in a channel whose bottom slope is 0.5° and whose cross section is as shown in Fig. P13–132. The dimensions and the Manning coefficients for the surfaces of different subsections are
Consider two identical channels, one rectangular of bottom width b and one circular of diameter D, with identical flow rates, bottom slopes, and surface linings. If the flow height in the rectangular
Consider water flow through a V-shaped channel. Determine the angle θ the channel makes from the horizontal for which the flow is most efficient.FIGURE P13–134 Ө y
The flow rate of water in a 6-m-wide rectangular channel is to be measured using a 1.1-m-high sharp-crested rectangular weir that spans across the channel. If the head above the weir crest is 0.60 m
A rectangular channel with unfinished concrete surfaces is to be built to discharge water uniformly at a rate of 200 ft3/s. For the case of best cross section, determine the bottom width of the
Repeat Prob. 13–136E for the case of a trapezoidal channel of best cross section.Data Prob. 13–136EA rectangular channel with unfinished concrete surfaces is to be built to discharge water
Consider two identical 15-ft-wide rectangular channels each equipped with a 3-ft-high full-width weir, except that the weir is sharp-crested in one channel and broad-crested in the other. For a flow
The Archimedes number listed in Table 7–5 is appropriate for buoyant particles in a fluid. Do a literature search or an Internet search and find an alternative definition of the Archimedes number
Consider steady, laminar, fully developed, two dimensional Poiseuille flow—flow between two infinite parallel plates separated by distance h, with both the top plate and bottom plate stationary,
Consider the steady, laminar, fully developed, two dimensional Poiseuille flow of Prob. 7–95. The maximum velocity umax occurs at the center of the channel. (a) Generate a dimensionless
The pressure drop ΔP = P1 – P2 through a long section of round pipe can be written in terms of the shear stress τw along the wall. Shown in Fig. P7–97 is the shear stress acting by the wall on
Oftentimes it is desirable to work with an established dimensionless parameter, but the characteristic scales available do not match those used to define the parameter. In such cases, we create the

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