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engineering
engineering fluid mechanics
Questions and Answers of
Engineering Fluid Mechanics
A uniform flow of \(110,000 \mathrm{ft}^{3} / \mathrm{s}\) is measured in a natural channel that is approximately rectangular in shape with a \(2650-\mathrm{ft}\) width and \(17.5-\mathrm{ft}\)
A 2-m-diameter pipe made of finished concrete lies on a slope of 1-m elevation change per \(1000-\mathrm{m}\) horizontal distance. Determine the flowrate when the pipe is half full.
By what percent is the flowrate reduced in the rectangular channel shown in Fig. P10.37 because of the addition of the thin center board? All surfaces are of the same material.Figure P10.37 b/2 b/2-
A large trapezoidal channel cut through stone has side slopes of 1:1 and a bed width of \(291 \mathrm{ft}\). Find the uniform flow in the channel when the flow depth is \(30.4 \mathrm{ft}\) and the
The great Kings River flume in Fresno County, California, was used from 1890 to 1923 to carry logs from an elevation of \(4500 \mathrm{ft}\) where trees were cut to an elevation of \(300
An unfinished concrete rectangular channel is \(5 \mathrm{~m}\) wide and has a slope of \(0.50^{\circ}\). The water is \(0.5 \mathrm{~m}\) deep. Find the discharge rate for uniform flow.
A trapezoidal channel with a bottom width of \(3.0 \mathrm{~m}\) and sides with a slope of 2:1 (horizontal:vertical) is lined with fine gravel \((n=0.020)\) and is to carry \(10 \mathrm{~m}^{3} /
Water flows in a 2-m-diameter finished concrete pipe so that it is completely full and the pressure is constant all along the pipe. If the slope is \(S_{0}=0.005\), determine the flowrate by using
A round concrete storm sewer pipe used to carry rainfall runoff from a parking lot is designed to be half full when the rainfall rate is a steady \(1 \mathrm{in}\)./hr. Will this pipe be able to
Find the discharge per unit width for a wide channel having a bottom slope of 0.00015 . The normal depth is \(0.003 \mathrm{~m}\). Assume laminar flow and justify the assumption. The fluid is
Water flows down a wide rectangular channel having Manning's \(n=0.015\) and bottom slope \(=0.0015\). Find the rate of discharge and normal depth for critical flow conditions.
The smooth, concrete-lined channel shown in Fig. P10.46 is built on a slope of \(2 \mathrm{~m} / \mathrm{km}\). Determine the flowrate if the depth is \(y=1.5 \mathrm{~m}\).Figure P10.46 -6 m- 1.0 m
At a given location, under normal conditions a river flows with a Manning coefficient of 0.030 , and a cross section as indicated in Fig. P10.47a. During flood conditions at this location, the river
The channel in Fig. P10.48 has two floodplains as shown. Find the discharge if the center channel is lined with brick and the two floodplains are lined with cobblestones. The slope \(S_{0}\) is
Determine the flowrate for the symmetrical channel shown in Fig. P10.66 if the bottom is smooth concrete and the sides are weedy. The bottom slope is \(S_{0}=0.001\).Fig. P10.66 4 ft 3 ft. 12 ft-
The Wide World of Fluids article titled "Done without GPS or Lasers,". Determine the number of gallons of water delivered per day by a rubble masonry, \(1.2-\mathrm{m}\)-wide aqueduct laid on an
An old, rough-surfaced, 2-m-diameter concrete pipe with a Manning coefficient of 0.025 carries water at a rate of \(5.0 \mathrm{~m}^{3} / \mathrm{s}\) when it is half full. It is to be replaced by a
Four sewer pipes of \(0.5-\mathrm{m}\) diameter join to form one pipe of diameter \(D\). If the Manning coefficient, \(n\), and the slope are the same for all of the pipes, and if each pipe flows
The spillway of a dam is \(20.0 \mathrm{ft}\) wide and has a flow rate of \(5000 \mathrm{ft}^{3} / \mathrm{s}\). The spillway makes an angle of \(30^{\circ}\) with the horizontal. Find the vertical
The flowrate in the clay-lined channel \((n=0.025)\) shown in Fig. P10.54 is to be \(300 \mathrm{ft}^{3} / \mathrm{s}\). To prevent erosion of the sides, the velocity must not exceed \(5 \mathrm{ft}
The flowrate in the clay-lined channel \((n=0.025)\) shown in Fig. P10.54 is to be \(300 \mathrm{ft}^{3} / \mathrm{s}\). To prevent erosion of the sides, the velocity must not exceed \(5 \mathrm{ft}
A rectangular, unfinished concrete channel of \(28-\mathrm{ft}\) width is laid on a slope of \(8 \mathrm{ft} / \mathrm{mi}\). Determine the flow depth and Froude number of the flow if the flowrate is
An engineer is to design a channel lined with planed wood to carry water at a flowrate of \(2 \mathrm{~m}^{3} / \mathrm{s}\) on a slope of \(10 \mathrm{~m} / 800 \mathrm{~m}\). The channel cross
Find the diameter required for reinforced concrete pipe laid at a slope of 0.001 and required to carry a uniform flow of \(19.3 \mathrm{ft}^{3} / \mathrm{sec}\) when the depth is \(75 \%\) of the
A major river is divided into three parts or courses-the upper course, the middle course, and the lower course. The slope is \(70 \mathrm{ft}\) per mile in the upper course, \(10 \mathrm{ft}\) per
Two canals join to form a larger canal as shown in Video V10.6 and Fig. P10.62. Each of the three rectangular canals is lined with the same material and has the same bottom slope. The water depth in
Water flows uniformly at a depth of \(1 \mathrm{~m}\) in a channel that is \(5 \mathrm{~m}\) wide as shown in Fig. P10.63. Further downstream, the channel cross section changes to that of a square of
Water flows \(1 \mathrm{~m}\) deep in a 2 -m-wide finished concrete channel. Determine the slope if the flowrate is \(3 \mathrm{~m}^{3} / \mathrm{s}\).
Uniform flow in a sluggish channel having a nearly rectangular cross section that is \(498 \mathrm{ft}\) wide and \(16.5 \mathrm{ft}\) deep carries a flow of \(8,250 \mathrm{ft}^{3} / \mathrm{s}\).
To prevent weeds from growing in a clean earthen-lined canal, it is recommended that the velocity be no less than \(2.5 \mathrm{ft} / \mathrm{s}\). For the symmetrical canal shown in Fig. P10.66,
The symmetrical channel shown in Fig. P10.66 is dug in sandy loam soil with \(n=0.020\). For such surface material it is recommended that to prevent scouring of the surface the average velocity be no
Figure P10.68 shows a cross section of an aqueduct that carries water at \(50 \mathrm{~m}^{3} / \mathrm{s}\). The value of Manning's \(n\) is 0.015 . Find the bottom slope.Figure P10.68 45 4.0 m
The depth downstream of a sluice gate in a rectangular wooden channel of width \(5 \mathrm{~m}\) is \(0.60 \mathrm{~m}\). If the flowrate is \(18 \mathrm{~m}^{3} / \mathrm{s}\), determine the channel
A 50-ft-long aluminum gutter (Manning coefficient \(n=0.011\) ) on a section of a roof is to handle a flowrate of \(0.15 \mathrm{ft}^{3} / \mathrm{s}\) during a heavy rainstorm. The cross section of
Consider the flow down a prismatic channel having a trapezoidal cross section of base width \(b\) and top width \(b+2 y\) \(\cos \theta \cot \phi\). The channel bottom makes an angle \(\theta\) with
Consider the flow down a prismatic channel having a rectangular cross section of width \(b\). The channel bottom makes an angle \(\theta\) with the horizontal. Show that\[ \frac{d y}{d x}=\frac{\tan
Water flows at \(150 \mathrm{ft}^{3} / \mathrm{s}\) in a 3 - \(\mathrm{ft}\)-wide rectangular cleanearth irrigation canal. The canal slope is \(0.275^{\circ}\). At one point, the water depth is \(3
Water flows upstream of a hydraulic jump with a depth of \(0.5 \mathrm{~m}\) and a velocity of \(6 \mathrm{~m} / \mathrm{s}\). Determine the depth of the water downstream of the jump.
A \(5.0-\mathrm{m}\)-wide channel has a slope of 0.004 , a \(8.0-\mathrm{m}^{3} / \mathrm{s}\). water flow rate, and a water depth \(1.5 \mathrm{~m}\) after a hydraulic jump. Find the water depth
The water depths upstream and downstream of a hydraulic jump are 0.3 and \(1.2 \mathrm{~m}\), respectively. Determine the upstream velocity and the power dissipated if the channel is \(50
Under appropriate conditions, water flowing from a faucet, onto a flat plate, and over the edge of the plate can produce a circular hydraulic jump as shown in Fig. P10.77 and Video V10.12. Consider a
At a given location in a 12-ft-wide rectangular channel the flowrate is \(900 \mathrm{ft}^{3} / \mathrm{s}\) and the depth is \(4 \mathrm{ft}\). Is this location upstream or downstream of the
A rectangular channel \(3.0 \mathrm{~m}\) wide has a flow rate of 5.0 \(\mathrm{m}^{3} / \mathrm{s}\) with a normal depth of \(0.50 \mathrm{~m}\). The flow then encounters a dam that rises \(0.25
A \(90^{\circ}\) triangular flume has sides \(2.0 \mathrm{~m}\) wide, a water flow rate of \(1.0 \mathrm{~m}^{3} / \mathrm{s}\), and a depth of \(0.50 \mathrm{~m}\). Find the depth after a hydraulic
Water flows in a rectangular channel with velocity \(V=6 \mathrm{~m} / \mathrm{s}\). A gate at the end of the channel is suddenly closed so that a wave (a moving hydraulic jump) travels upstream with
A hydraulic engineer wants to analyze steady flow in a rectangular channel featuring a hydraulic jump immediately downstream from a sluice gate that is open to a vertical clearance of \(3
The Wide World of Fluids article titled "Grand Canyon Rapids Building.". During the flood of 1983, a large hydraulic jump formed at "Crystal Rapid" on the Colorado River. People rafting the river at
A rectangular sharp-crested weir is used to measure the flowrate in a channel of width \(10 \mathrm{ft}\). It is desired to have the upstream channel flow depth be \(6 \mathrm{ft}\) when the flowrate
Water flows over a sharp-crested triangular weir with \(\theta=90^{\circ}\). The head range covered is \(0.20 \leq H \leq 1.0 \mathrm{ft}\) and the accuracy in the measurement of the head, \(H\), is
Water flows over the sharp-crested weir shown in Fig. P10.86. The weir plate cross section consists of a semicircle and a rectangle. Plot a graph of the estimated flowrate, \(Q\), as a function of
Water flows over a broad-crested weir that has a width of \(4 \mathrm{~m}\) and a height of \(P_{w}=1.5 \mathrm{~m}\). The free-surface well upstream of the weir is at a height of \(0.5 \mathrm{~m}\)
An engineering laboratory experiment uses a triangular weir in an open channel to measure flow rate. The nominal weir angle is \(90^{\circ}\). In a certain test, the head of water above the weir was
Water flows under a sluice gate in a 60 -ft-wide finished concrete channel as is shown in Fig. P10.89. Determine the flowrate. If the slope of the channel is \(2.5 \mathrm{ft} / 200 \mathrm{ft}\),
Water flows under a sluice gate in a channel of 10 -ft width. If the upstream depth remains constant at \(5 \mathrm{ft}\), plot a graph of flowrate as a function of the distance between the gate and
A flow of \(873 \mathrm{ft}^{3} / \mathrm{s}\) passes under a sluice gate in a rectangular channel having a gradual contraction in width from \(80 \mathrm{ft}\) to \(52 \mathrm{ft}\). The channel bed
Under normal circumstances is the airflow though your trachea (your windpipe) laminar or turbulent? List all assumptions and show all calculations.
Rainwater runoff from a parking lot flows through a 3 -ft-diameter pipe, completely filling it. Whether flow in a pipe is laminar or turbulent depends on the value of the Reynolds number. Would you
Blue and yellow streams of paint at \(60^{\circ} \mathrm{F}\) (each with a density of \(1.6 \mathrm{slugs} / \mathrm{ft}^{3}\) and a viscosity 1000 times greater than water) enter a pipe with an
Air at \(200^{\circ} \mathrm{F}\) flows at standard atmospheric pressure in a pipe at a rate of \(0.08 \mathrm{lb} / \mathrm{s}\). Determine the minimum diameter allowed if the flow is to be laminar.
To cool a given room it is necessary to supply \(4 \mathrm{ft}^{3} / \mathrm{s}\) of air through an 8-in.-diameter pipe. Approximately how long is the entrance length in this pipe?
The flow of water in a 3-mm-diameter pipe is to remain laminar. Plot a graph of the maximum flowrate allowed as a function of temperature for \(0
The pressure distribution measured along a straight, horizontal portion of a 50-mm-diameter pipe attached to a tank is shown in the table below. Approximately how long is the entrance length? In the
The Wide World of Fluids article titled "Nanoscale Flows,".(a) Water flows in a tube that has a diameter of \(D=0.1 \mathrm{~m}\). Determine the Reynolds number if the average velocity is 10
For fully developed laminar pipe flow in a circular pipe, the velocity profile is given by \(u(r)=2\left(1-r^{2} / R^{2}\right)\) in \(\mathrm{m} / \mathrm{s}\), where \(R\) is the inner radius of
A viscous fluid flows in a \(0.10-\mathrm{m}\)-diameter pipe such that its velocity measured \(0.012 \mathrm{~m}\) away from the pipe wall is \(0.8 \mathrm{~m} / \mathrm{s}\). If the flow is laminar,
The wall shear stress in a fully developed flow portion of a 12 -in.-diameter pipe carrying water is \(1.85 \mathrm{lb} / \mathrm{ft}^{2}\). Determine the pressure gradient, \(\partial p / \partial
The pressure drop needed to force water through a horizontal 1-in.-diameter pipe is \(0.60 \mathrm{psi}\) for every 12 -ft length of pipe. Determine the shear stress on the pipe wall. Determine the
Repeat Problem 8.12 if the pipe is on a \(20^{\circ}\) hill. Is the flow up or down the hill? Explain.
Water flows in a constant-diameter pipe with the following conditions measured: At section(a) \(p_{a}=32.4 \mathrm{psi}\) and \(z_{a}=56.8 \mathrm{ft}\); at section(b) \(p_{b}=29.7 \mathrm{psi}\) and
Glycerin at \(20^{\circ} \mathrm{C}\) flows upward in a vertical 75 -mm-diameter pipe with a centerline velocity of \(1.0 \mathrm{~m} / \mathrm{s}\). Determine the head loss and pressure drop in a
Water at \(60{ }^{\circ} \mathrm{F}\) flows at a rate of \(4.0 \mathrm{gal} / \mathrm{min}\) through a 6 -in. I.D. plastic pipe. The pipe is \(500 \mathrm{ft}\) long and rises a vertical height of
At time \(t=0\) the level of water in tank \(A\) shown in Fig. P8.18 is \(2 \mathrm{ft}\) above that in \(\operatorname{tank} B\). Plot the elevation of the water in tank \(A\) as a function of time
A fluid flows through a horizontal 0.1-in.-diameter pipe. When the Reynolds number is 1500 , the head loss over a \(20-\mathrm{ft}\) length of the pipe is \(6.4 \mathrm{ft}\). Determine the fluid
Asphalt at \(120^{\circ} \mathrm{F}\), considered to be a Newtonian fluid with a viscosity 80,000 times that of water and a specific gravity of 1.09, flows through a pipe of diameter \(2.0
Oil of \(S G=0.87\) and a kinematic viscosity \(u=2.2 \times 10^{-4}\) \(\mathrm{m}^{2} / \mathrm{s}\) flows through the vertical pipe shown in Fig. P8.21 at a rate of \(4 \times 10^{-4}
A liquid with \(S G=0.96, \mu=9.2 \times 10^{-4} \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\), and vapor pressure \(p_{u}=1.2 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}\) (abs) is drawn into the
A 3-in. schedule 40 commercial steel pipe (with an actual inside diameter of 3.068 in.) carries \(210^{\circ} \mathrm{F}\) SAE 40 crankcase oil at the rate of \(6.0 \mathrm{gal} / \mathrm{min}\). The
A 3-in. schedule 40 commercial steel pipe (with an actual inside diameter of 3.068 in.) carries \(210^{\circ} \mathrm{F}\) SAE 40 crankcase oil at the rate of \(6.0 \mathrm{gal} / \mathrm{min}\). The
Water at \(20{ }^{\circ} \mathrm{C}\) flows down a vertical pipe with no pressure drop. Find the range of pipe diameters \(D\) (if any) for which the flow is definitely laminar.
A person is donating blood. The pint bag in which the blood is collected is initially flat and is at atmospheric pressure. Neglect the initial mass of air in the 1/8-in. I.D., \(4 \mathrm{ft}\)-long
For oil \(\left(S G=0.86, \mu=0.025 \mathrm{Ns} / \mathrm{m}^{2}\right.\) ) flow of \(0.2 \mathrm{~m}^{3} / \mathrm{s}\) through a round pipe with diameter of \(500 \mathrm{~mm}\), determine the
As shown in Fig. P8.28, the velocity profile for laminar flow in a pipe is quite different from that for turbulent flow. With laminar flow the velocity profile is parabolic; with turbulent flow at
Water at \(10{ }^{\circ} \mathrm{C}\) flows through a smooth \(60-\mathrm{mm}\)-diameter pipe with an average velocity of \(8 \mathrm{~m} / \mathrm{s}\). Would a layer of rust of height \(0.005
When soup is stirred in a bowl, there is considerable turbulence in the resulting motion. From a very simplistic standpoint, this turbulence consists of numerous intertwined swirls, each involving a
Water at \(60^{\circ} \mathrm{F}\) flows through a 6-in.-diameter pipe with an average velocity of \(15 \mathrm{ft} / \mathrm{s}\). Approximately what is the height of the largest roughness element
Water is pumped between two tanks as shown in Fig. P8.32. The energy line is as indicated. Is the fluid being pumped from \(A\) to \(B\) or \(B\) to \(A\) ? Explain. Which pipe has the larger
A person with no experience in fluid mechanics wants to estimate the friction factor for 1-in.-diameter galvanized iron pipe at a Reynolds number of 8,000 . The person stumbles across the simple
Water flows through a horizontal plastic pipe with a diameter of \(0.2 \mathrm{~m}\) at a velocity of \(10 \mathrm{~cm} / \mathrm{s}\). Determine the pressure drop per meter of pipe and the power
Air at standard conditions flows through an 8-in.-diameter, 14.6-ft-long, straight duct with the velocity versus head loss data indicated in the following table. Determine the average friction factor
Water flows through a horizontal 60-mm-diameter galvanized iron pipe at a rate of \(0.02 \mathrm{~m}^{3} / \mathrm{s}\). If the pressure drop is \(135 \mathrm{kPa}\) per \(10 \mathrm{~m}\) of pipe,
Water flows at a rate of 10 gallons per minute in a new horizontal 0.75-in.-diameter galvanized iron pipe. Determine the pressure gradient, \(\Delta p / \ell\), along the pipe.
Carbon dioxide at a temperature of \(0{ }^{\circ} \mathrm{C}\) and a pressure of \(600 \mathrm{kPa}\) (abs) flows through a horizontal 40-mm-diameter pipe with an average velocity of \(2 \mathrm{~m}
Blood (assume \(\mu=4.5 \times 10^{-5} \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}, S G=1.0\) ) flows through an artery in the neck of a giraffe from its heart to its head at a rate of \(2.5
A 40-m-long, 12-mm-diameter pipe with a friction factor of 0.020 is used to siphon \(30{ }^{\circ} \mathrm{C}\) water from a tank as shown in Fig. P8.42. Determine the maximum value of \(h\) allowed
Gasoline flows in a smooth pipe of \(40-\mathrm{mm}\) diameter at a rate of \(0.001 \mathrm{~m}^{3} / \mathrm{s}\). If it were possible to prevent turbulence from occurring, what would be the ratio
A 3-ft-diameter duct is used to carry ventilating air into a vehicular tunnel at a rate of \(9000 \mathrm{ft}^{3} / \mathrm{min}\). Tests show that the pressure drop is \(1.5 \mathrm{in}\). of water
H. Blasius correlated data on turbulent friction factor in smooth pipes. His equation \(f_{\text {smooth }} \approx 0.3164 \mathrm{Re}^{-1 / 4}\) is reasonably accurate for Reynolds numbers between
Von Karman suggested that the wholly turbulent friction factor be expressed by the equation\[ f=\frac{1}{4[0.57-\log (\varepsilon / D)]^{2}} \]where \(\varepsilon\) is the absolute roughness of the
The Swamee and Jain formula for the friction factor is\[ f=\frac{0.25}{\left[\log \left(\varepsilon / 3.7 D+5.74 / \mathrm{Re}^{0.9}\right)\right]^{2}} \]Compare this equation for \(\varepsilon /
The Haaland formula for the friction factor is\[ f=\frac{0.3086}{\left\{\log \left[6.9 / \operatorname{Re}+(\varepsilon / 3.7 D)^{1.11}\right]\right\}^{2}} \]Compare this equation for \(f\) for
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