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engineering
engineering fluid mechanics

Munson Young And Okiishi's Fundamentals Of Fluid Mechanics 8th Edition Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein - Solutions

A hot-air balloon roughly spherical in shape has a volume of 70,000 \(\mathrm{ft}^{3}\) and a weight of \(500 \mathrm{lb}\) (including passengers, basket, balloon fabric, etc.). If the outside air temperature is \(80^{\circ} \mathrm{F}\) and the temperature within the balloon is \(165^{\circ}
It is often assumed that "sharp objects can cut through the air better than blunt ones." Based on this assumption, the drag on the object shown in Fig. P9.59 should be less when the wind blows from right to left than when it blows from left to right. Experiments show that the opposite is true.
An object falls at a rate of \(100 \mathrm{ft} / \mathrm{s}\) immediately prior to the time that the parachute attached to it opens. The final descent rate with the chute open is \(10 \mathrm{ft} / \mathrm{s}\). Calculate and plot the speed of falling as a function of time from when the chute
Estimate the velocity with which you would contact the ground if you jumped from an airplane at an altitude of 5,000 ft and(a) air resistance is negligible,(b) air resistance is important, but you forgot your parachute, (c) you use a 25 -ft-diameter parachute.
As is discussed in Section 9.3, the drag on a rough golf ball may be less than that on an equal-sized smooth ball. Does it follow that a \(10-\mathrm{m}\)-diameter spherical water tank resting on a \(20-\mathrm{m}\)-tall support should have a rough surface so as to reduce the moment needed at the
A 12-mm-diameter cable is strung between a series of poles that are \(50 \mathrm{~m}\) apart. Determine the horizontal force this cable puts on each pole if the wind velocity is \(30 \mathrm{~m} / \mathrm{s}\).
A strong wind can blow a golf ball off the tee by pivoting it about point 1 as shown in Fig. P9.64. Determine the wind speed necessary to do this.Figure P9.64 U (1) 40.20 0.20 in. Radius = 0.845 in. Weight 0.0992 lb
A 22 in. by 34 in. speed limit sign is supported on a 3 -in.-wide, 5 -ft-long pole. Estimate the bending moment in the pole at ground level when a 30 -mph wind blows against the sign. List any assumptions used in your calculations.
A \(20-\mathrm{m} / \mathrm{s}\) wind blows against a \(20-\mathrm{m}\)-tall, \(0.12-\mathrm{m}\)-diameter flag pole.(a) Determine the anchoring moment at the base of the pole.(b) Determine the anchoring moment if a \(2-\mathrm{m}\) by \(2.5-\mathrm{m}\) flag is attached to the top of the pole. See
During a flash flood, water rushes over a road as shown in Fig. P9. 67 with a speed of \(12 \mathrm{mph}\). Estimate the maximum water depth, \(h\), that would allow a car to pass without being swept away. List all assumptions and show all calculations.Figure P9.67 U = 12 mph h
With the rider in the racing position, how much more power is required to pedal a bicycle at \(15 \mathrm{mph}\) into a \(20-\mathrm{mph}\) head-wind than at \(15 \mathrm{mph}\) through still air? Pedaling at \(15 \mathrm{mph}\) in still air, how much more power is required for an upright position
Estimate the wind velocity necessary to knock over a \(20-\mathrm{lb}\) garbage can that is \(3 \mathrm{ft}\) tall and \(2 \mathrm{ft}\) in diameter. List your assumptions.
On a day without any wind, your car consumes \(x\) gallons of gasoline when you drive at a constant speed, \(U\), from point \(A\) to point \(B\) and back to point \(A\). Assume that you repeat the journey, driving at the same speed, on another day when there is a steady wind blowing from \(B\) to
The structure shown in Fig. P9.71 consists of three cylindrical support posts to which an elliptical flat plate sign is attached. Estimate the drag on the structure when a \(50-\mathrm{mph}\) wind blows against it.Figure P9.71 16 ft Adrianna's Petting Zoo 5 ft 0.6 ft 15 ft 0.8 ft- 15 ft 1 ft- 15 ft
A 25-ton (50,000-lb) truck coasts down a steep \(7 \%\) mountain grade without brakes, as shown in Fig. P9.72. The truck's ultimate steady-state speed, \(V\), is determined by a balance between weight, rolling resistance, and aerodynamic drag. Determine \(V\) if the rolling resistance for a truck
Phil's Pizza Parlor decides to place a thin, rectangular, plastic sign on top of its delivery van as shown in Fig. P9.73. The sign measures \(2 \mathrm{ft}\) by \(5 \mathrm{ft}\). (a) Estimate the extra power required to drive the van in standard still air at \(35 \mathrm{mph}\) if the sign faces
As shown in Fig. P9.74, the aerodynamic drag on a truck can be reduced by the use of appropriate air deflectors. A reduction in drag coefficient from \(C_{D}=0.96\) to \(C_{D}=0.70\) corresponds to a reduction of how many horsepower needed at a highway speed of \(65 \mathrm{mph}\)?Fig. P9.74
A full-sized automobile has a frontal area of \(24 \mathrm{ft}^{2}\), and a compact car has a frontal area of \(13 \mathrm{ft}^{2}\). Both have a drag coefficient of 0.5 based on the frontal area. Find the horsepower required to move each automobile along a level road in still air at \(55
Estimate the energy required for an average person (see Fig. 9.32) to run a mile in 4 minutes in still standard air. Compare your estimate if you instead modeled the person as a cylinder \(6 \mathrm{ft}\) tall and \(2 \mathrm{ft}\) in diameter.Fig. 9.32 Shape Reference area Parachute Frontal area
As shown in Fig. P9.77, a vertical wind tunnel can be used for skydiving practice. Estimate the vertical wind speed needed if a 160-lb person is to be able to "float" motionless when the person(a) curls up as in a crouching position (b) lies flat. See Fig. 9.30 for appropriate drag coefficient
Compare the rise velocity of an \(\frac{1}{8}\)-in.-diameter air bubble in water to the fall velocity of an \(\frac{1}{8}\)-in.-diameter water drop in air. Assume each to behave as a solid sphere.
A 50-lb box shaped like a 1-ft cube falls from the cargo hold of an airplane at an altitude of \(30,000 \mathrm{ft}\). If the drag coefficient of the falling box is 1.2, determine the time it takes for the box to hit the ocean. Assume that it falls at the terminal velocity corresponding to its
A 500-N cube of specific gravity \(S G=1.8\) falls through water at a constant speed \(U\). Determine \(U\) if the cube falls (a) as oriented in Fig. P9.80a, (b) as oriented in Fig. P9.80b. Figure P9.80 (9) 8 (D)
The helium-filled balloon shown in Fig P9.81 is to be used as a wind-speed indicator. The specific weight of the helium is \(y=0.011 \mathrm{lb} / \mathrm{ft}^{3}\), the weight of the balloon material is \(0.20 \mathrm{lb}\), and the weight of the anchoring cable is negligible. Plot a graph of
A 0.30-m-diameter cork ball \((S G=0.21)\) is tied to an object on the bottom of a river as is shown in Fig. P9.82. Estimate the speed of the river current. Neglect the weight of the cable and the drag on it.Figure P9.82 U 30
A shortwave radio antenna is constructed from circular tubing, as is illustrated in Fig. P9.83. Estimate the wind force on the antenna in a \(100-\mathrm{km} / \mathrm{hr}\) wind.Figure P9.83 0.6 m 10-mm diameter 1 m long 20-mm diameter 1.5 m long 0.5 m 0.25 m 40-mm diameter 5 m long
Estimate the wind force on your hand when you hold it out of your car window while driving \(55 \mathrm{mph}\). Repeat your calculations if you were to hold your hand out of the window of an airplane flying \(550 \mathrm{mph}\).
Estimate the energy that a runner expends to overcome aerodynamic drag while running a complete marathon race. This expenditure of energy is equivalent to climbing a hill of what height? List all assumptions and show all calculations.
A 2-mm-diameter meteor of specific gravity 2.9 has a speed of \(6 \mathrm{~km} / \mathrm{s}\) at an altitude of \(50,000 \mathrm{~m}\) where the air density is \(1.03 \times\) \(10^{-3} \mathrm{~kg} / \mathrm{m}^{3}\). If the drag coefficient at this large Mach number condition is 1.5, determine
Air flows past two equal sized spheres (one rough, one smooth) that are attached to the arm of a balance as is indicated in Fig. P9.87. With \(U=0\) the beam is balanced. What is the minimum air velocity for which the balance arm will rotate clockwise?Figure P9.87 D= 0.1 m Smooth sphere Rough
A 2-in.-diameter sphere weighing \(0.14 \mathrm{lb}\) is suspended by the jet of air shown in Fig. P9.88. The drag coefficient for the sphere is 0.5. Determine the reading on the pressure gage if friction and gravity effects can be neglected for the flow between the pressure gage and the nozzle
A smooth orange ball weighs \(\frac{1}{64} \mathrm{lb}\) (at sea level) and has a diameter of \(1.5 \mathrm{in}\). The discharge of a vacuum cleaner is directed upward and supports the ball \(\frac{1}{2}\) in. If the hose inside diameter is 4.0 in., estimate the volume flow rate through the vacuum
A \(60 \mathrm{mph}\) wind blows against a football stadium scoreboard that is \(36 \mathrm{ft}\) tall, \(80 \mathrm{ft}\) wide, and \(8 \mathrm{ft}\) thick (parallel to the wind). Estimate the wind force on the scoreboard. See Fig. 9.30 for drag coefficient data.Fig. 9.30 Shape D R Square rod with
A marine location marker is a smoke-producing device usually dropped from an airplane and used to mark a reference point in the ocean. One is being tested in a wind tunnel to determine the drag force when it is carried by an airplane at a velocity of \(200 \mathrm{mph}\). The marker is a cylinder
The United Nations Building in New York is approximately \(87.5 \mathrm{~m}\) wide and \(154 \mathrm{~m}\) tall.(a) Determine the drag on this building if the drag coefficient is and the wind speed is a uniform \(20 \mathrm{~m} / \mathrm{s}\).(b) Repeat your calculations if the velocity profile
An airplane flies at \(150 \mathrm{~km} / \mathrm{hr}\).(a) The airplane is towing a banner that is \(b=0.8 \mathrm{~m}\) tall and \(\ell=25 \mathrm{~m}\) long. If the drag coefficient based on area \(b \ell\) is \(C_{D}=0.06\), estimate the power required to tow the banner.(b) For comparison,
The paint stirrer shown in Fig. P9.94 consists of two circular disks attached to the end of a thin rod that rotates at \(80 \mathrm{rpm}\). The specific gravity of the paint is \(S G=1.1\) and its viscosity is \(\mu=2 \times\) \(10^{-2} \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}\). Estimate the
If the wind becomes strong enough, it is "impossible" to paddle a canoe into the wind. Estimate the wind speed at which this will happen. List all assumptions and show all calculations.
By appropriate streamlining, the drag coefficient for an airplane is reduced by \(12 \%\) while the frontal area remains the same. For the same power output, by what percentage is the flight speed increased?
As indicated in Fig. P9.97, the orientation of leaves on a tree is a function of the wind speed, with the tree becoming "more streamlined" as the wind increases. The resulting drag coefficient for the tree (based on the frontal area of the tree, \(H W\) ) as a function of Reynolds number (based on
As indicated in Fig. P9.97, the orientation of leaves on a tree is a function of the wind speed, with the tree becoming "more streamlined" as the wind increases. The resulting drag coefficient for the tree (based on the frontal area of the tree, \(H W\) ) as a function of Reynolds number (based on
The Wide World of Fluids article "Dimpled Baseball Bats,". How fast must a 3.5-in.-diameter, dimpled baseball bat move through the air in order to take advantage of drag reduction produced by the dimples on the bat? Although there are differences, assume the bat (a cylinder) acts the same as a golf
The Wide World of Fluids article "At 12,600 mpg It Doesn't Cost Much to 'Fill 'er Up,"'. (a) Determine the power it takes to overcome aerodynamic drag on a small \(\left(6 \mathrm{ft}^{2}\right.\) cross section), streamlined ( \(C_{D}=0.12\) ) vehicle traveling \(15 \mathrm{mph}\). (b) Compare the
A rectangular wing with an aspect ratio of 6 is to generate \(1000 \mathrm{lb}\) of lift when it flies at a speed of \(200 \mathrm{ft} / \mathrm{s}\). Determine the length of the wing if its lift coefficient is 1.0.
A 1.2-lb kite with an area of \(6 \mathrm{ft}^{2}\) flies in a \(20-\mathrm{ft} / \mathrm{s}\) wind such that the weightless string makes an angle of \(55^{\circ}\) relative to the horizontal. If the pull on the string is \(1.5 \mathrm{lb}\), determine the lift and drag coefficients based on the
A Piper Cub airplane has a gross weight of \(1750 \mathrm{lb}\), a cruising speed of \(115 \mathrm{mph}\), and a wing area of \(179 \mathrm{ft}^{2}\). Determine the lift coefficient of this airplane for these conditions.
A light aircraft with a wing area of \(200 \mathrm{ft}^{2}\) and a weight of \(2000 \mathrm{lb}\) has a lift coefficient of 0.40 and a drag coefficient of 0.05. Determine the power required to maintain level flight.
An airplane weighs \(320,000 \mathrm{lb}\), has a wing area of \(2800 \mathrm{ft}^{2}\), and has a wing length of \(140 \mathrm{ft}\). The atmospheric pressure and temperature are \(14.67 \mathrm{psia}\) and \(60^{\circ} \mathrm{F}\), respectively. The airplane is moving along a runway at \(200
As shown in V9.25 and Fig. P9.105, a spoiler (i.e., an upside-down airfoil) is mounted above the rear wheels of a race car to produce negative lift (i.e., downforce), thereby improving tractive force. The spoiler's airfoil is angled \(10^{\circ}\) with the race track and has lift and drag
The wings of old airplanes are often strengthened by the use of wires that provided cross-bracing as shown in Fig. P9.106. If the drag coefficient for the wings was 0.020(based on the planform area), determine the ratio of the drag from the wire bracing to that from the wings.Figure P9. 106 Speed:
A wing generates a lift \(\mathscr{L}\) when moving through sea-level air with a velocity \(U\). How fast must the wing move through the air at an altitude of \(10,000 \mathrm{~m}\) with the same lift coefficient if it is to generate the same lift?
A design group has two possible wing designs \((A\) and \(B\) ) for an airplane wing. The planform area of either wing is \(130 \mathrm{~m}^{2}\) and each must provide a lift of \(1,550,000 \mathrm{~N}\).Figure P9.108The airplane is to fly at \(700 \mathrm{~km} / \mathrm{hr}\) at an altitude of
Air blows over the flat-bottomed, two-dimensional object shown in Fig. P9.109. The shape of the object, \(y=y(x)\), and the fluid speed along the surface, \(u=u(x)\), are given in the table. Determine the lift coefficient for this object.Figure P9.109 =" (x)=n n
When air flows past the airfoil shown in Fig. P9.110, the velocity just outside the boundary layer, \(u\), is as indicated. Estimate the lift coefficient for these conditions.Figure P9.110 U 1.6 1.2 Lower surface 0.8 -Upper surface 0.4 NACA 632-015 0 0 0.2 0.4 4/7 49 0.6 0.8 1.0
A Boeing 747 aircraft weighing \(580,000 \mathrm{lb}\) when loaded with fuel and 100 passengers takes off with an airspeed of \(140 \mathrm{mph}\). With the same configuration (i.e., angle of attack, flap settings, etc.), what is its takeoff speed if it is loaded with 372 passengers? Assume each
Show that for unpowered flight (for which the lift, drag, and weight forces are in equilibrium) the glide slope angle, \(\theta\), is given by \(\tan \theta=C_{D} / C_{L}\).
A sail plane with a lift-to-drag ratio of 25 flies with a speed of \(50 \mathrm{mph}\). It maintains or increases its altitude by flying in thermals, columns of vertically rising air produced by buoyancy effects of nonuniformly heated air. What vertical airspeed is needed if the sail plane is to
If the lift coefficient for a Boeing 777 aircraft is 15 times greater than its drag coefficient, can it glide from an altitude of \(30,000 \mathrm{ft}\) to an airport \(80 \mathrm{mi}\) away if it loses power from its engines? Explain. (See Problem 9.112.)Problem 9.112A Boeing 747 aircraft weighing
Over the years there has been a dramatic increase in the flight speed \((U)\), altitude \((h)\), weight \((\mathcal{W})\), and wing loading ( \(W / A=\) weight divided by wing area) of aircraft. Use the data given in the table below to determine the lift coefficient for each of the aircraft listed.
If the required takeoff speed of a particular airplane is \(120 \mathrm{mi} / \mathrm{hr}\) at sea level, what will be required at Denver (elevation \(5000 \mathrm{ft}\) )? Use properties of the U.S. Standard Atmosphere.
The landing speed of a winged aircraft such as the Space Shuttle is dependent on the air density. By what percent must the landing speed be increased on a day when the temperature is \(110^{\circ} \mathrm{F}\) compared to a day when it is \(50^{\circ} \mathrm{F}\) ? Assume that the atmospheric
Commercial airliners normally cruise at relatively high altitudes \((30,000\) to \(35,000 \mathrm{ft}\) ). Discuss how flying at this high altitude (rather than 10,000 ft, for example) can save fuel costs.
A pitcher can pitch a "curve ball" by putting sufficient spin on the ball when it is thrown. A ball that has absolutely no spin will follow a "straight" path. A ball that is pitched with a very small amount of spin (on the order of one revolution during its flight between the pitcher's mound and
For many years, hitters have claimed that some baseball pitchers have the ability to actually throw a rising fastball. Assuming that a top major leaguer pitcher can throw a \(95-\mathrm{mph}\) pitch and impart an 1800-rpm spin to the ball, is it possible for the ball to actually rise? Assume the
A baseball leaves the pitcher's hand with horizontal velocity of \(90 \mathrm{mph}\) and travels a distance of \(45 \mathrm{ft}\). Neglect air drag and gravity, so the ball moves in a horizontal plane. The ball has a mass of \(5 \mathrm{oz}\), a circumference of 9 in., a rotational speed of \(1600
The Wide World of Fluids article "Learning from Nature,". As indicated in Fig. P9.122, birds can significantly alter their body shape and increase their planform area, \(A\), by spreading their wing and tail feathers, thereby reducing their flight speed. If during landing the planform area is
On a distant planet small-amplitude waves travel across a \(1-\mathrm{m}\)-deep pond with a speed of \(5 \mathrm{~m} / \mathrm{s}\). Determine the acceleration of gravity on the surface of that planet.
The flowrate per unit width in a wide channel is \(q=\) \(2.3 \mathrm{~m}^{2} / \mathrm{s}\). Is the flow subcritical or supercritical if the depth is(a) \(0.2 \mathrm{~m}\),(b) \(0.8 \mathrm{~m}\), (c) \(2.5 \mathrm{~m}\) ?
A rectangular channel \(3 \mathrm{~m}\) wide carries \(10 \mathrm{~m}^{3} / \mathrm{s}\) at a depth of \(2 \mathrm{~m}\). Is the flow subcritical or supercritical? For the same flowrate, what depth will give critical flow?
Do shallow waves propagate at the same speed in all fluids? Explain why or why not.
Waves on the surface of a tank are observed to travel at a speed of \(2 \mathrm{~m} / \mathrm{s}\). How fast would these waves travel if (a) the tank were in an elevator accelerating downward at a rate of \(4 \mathrm{~m} / \mathrm{s}^{2}\), (b) the tank accelerates horizontally at a rate of \(9.81
In flowing from section (1) to section (2) along an open channel, the water depth decreases by a factor of 2 and the Froude number changes from a subcritical value of 0.5 to a supercritical value of 3.0. Determine the channel width at (2) if it is \(12 \mathrm{ft}\) wide at (1).
Water flows with an average velocity of \(1.0 \mathrm{~m} / \mathrm{s}\) and a normal depth of \(0.5 \mathrm{~m}\) in a wide rectangular channel. Is the flow subcritical or supercritical?
A trout jumps, producing waves on the surface of a 0.8 -m-deep mountain stream. If it is observed that the waves do not travel upstream, what is the minimum velocity of the current?
Observations at a shallow sandy beach show that even though the waves several hundred yards out from the shore are not parallel to the beach, the waves often "break" on the beach nearly parallel to the shore as indicated in Fig. P10.9. Explain this behavior based on the wave speed \(c=(g y)^{1 /
(See The Wide World of Fluids article titled "Tsunami, the Nonstorm Wave,". Often when an earthquake shifts a segment of the ocean floor, a relatively small-amplitude wave of very long wavelength is produced. Such waves go unnoticed as they move across the open ocean; only when they approach the
What is the minimum water depth necessary for a 40 -ftwide stream to handle \(4000 \mathrm{ft}^{3} / \mathrm{s}\) if the flow is not supercritical?
Water flows in a 10-m-wide open channel with a flowrate of \(5 \mathrm{~m}^{3} / \mathrm{s}\). Determine the two possible depths if the specific energy of the flow is \(E=0.6 \mathrm{~m}\).
Water flows in a 10-ft-wide rectangular channel with a flowrate of \(200 \mathrm{ft}^{3} / \mathrm{s}\). Plot the specific energy diagram for this flow. Determine the two possible flowrates when the specific energy is \(6 \mathrm{ft}\).
Water flows in a rectangular channel at a rate of \(q=20 \mathrm{cfs} / \mathrm{ft}\). When a Pitot tube is placed in the stream, water in the tube rises to a level of \(4.5 \mathrm{ft}\) above the channel bottom. Determine the two possible flow depths in the channel. Illustrate this flow on a
Water flows in a 5 -ft-wide rectangular channel with a flowrate of \(Q=30 \mathrm{ft}^{3} / \mathrm{s}\) and an upstream depth of \(y_{1}=2.5 \mathrm{ft}\) as is shown in Fig. P10.15. Determine the flow depth and the surface elevation at section (2).Figure P10.15 (1) 0 0.2 ft (2)
Water flows over the bump in the bottom of the rectangular channel shown in Fig. P10.16 with a flowrate per unit width of \(q=4 \mathrm{~m}^{2} / \mathrm{s}\). The channel bottom contour is given by \(z_{B}=0.2 e^{-x^{2}}\), where \(z_{B}\) and \(x\) are in meters. The water depth far upstream of
Water in a rectangular channel flows into a gradual contraction section as is indicated in Fig. P10.17. If the flowrate is \(Q=25\) \(\mathrm{ft}^{3} / \mathrm{s}\) and the upstream depth is \(y_{1}=2 \mathrm{ft}\), determine the downstream depth, \(y_{2}\).Figure P10.17 b = 4 ft (1) Top view b = 3
A channel has a rectangular cross section, a width of \(40 \mathrm{~m}\), and a flow rate of \(4000 \mathrm{~m}^{3} / \mathrm{s}\). The normal water depth is \(20 \mathrm{~m}\). The flow then encounters a 4.0-m-high dam. Find the water depth directly above the dam if the flow is critical. Assume
Repeat Problem 10.17 if the upstream depth is \(y_{1}=0.5 \mathrm{ft}\). Assume that there are no losses between sections (1) and (2).
A rectangular channel has a gradual contraction in width from \(59 \mathrm{ft}\) to \(30 \mathrm{ft}\) and a bed level drop of \(6 \mathrm{in}\). below the upstream channel bed, which the increased velocity caused by the contraction scoured. If the upstream and downstream flow depths are both
Water flows in a rectangular channel with a flowrate per unit width of \(q=1.5 \mathrm{~m}^{2} / \mathrm{s}\) and a depth of \(0.5 \mathrm{~m}\) at section (1). The head loss between sections (1) and (2) is \(0.03 \mathrm{~m}\). Plot the specific energy diagram for this flow and locate states (1)
Water flows in a horizontal rectangular channel with a flowrate per unit width of \(q=10 \mathrm{ft}^{2} / \mathrm{s}\) and a depth of \(1.0 \mathrm{ft}\) at the downstream section (2). The head loss between section (1) upstream and section (2) is \(0.2 \mathrm{ft}\). Plot the specific energy
Water flows in a horizontal, rectangular channel with an initial depth of \(1 \mathrm{~m}\) and an initial velocity of \(4 \mathrm{~m} / \mathrm{s}\). Determine the depth downstream if losses are negligible. Note that there may be more than one solution.
A smooth transition section connects two rectangular channels as shown in Fig. P10.24. The channel width increases from 6.0 to \(7.0 \mathrm{ft}\), and the water surface elevation is the same in each channel. If the upstream depth of flow is \(3.0 \mathrm{ft}\), determine \(h\), the amount the
Water flows over a bump of height \(h=h(x)\) on the bottom of a wide rectangular channel as is indicated in Fig. P10.25. If energy losses are negligible, show that the slope of the water surface is given by \(d y / d x=-(d h / d x) /\left[1-\left(V^{2} / g y\right)\right]\), where \(V=V(x)\) and
Consider \(100 \mathrm{ft}^{3} / \mathrm{s}\) of water flowing down a rectangular channel measuring \(10 \mathrm{ft}\) wide. The normal depth is \(3.00 \mathrm{ft}\). A 4.0-ft-diameter pier is located in the channel. Find the water depth as it flows past the pier. Assume frictionless flow.
Water flows in the river shown in Fig. P10.27 with a uniform bottom slope. The total head at each section is measured by using Pitot tubes as indicated. Determine the value of \(d y / d x\) at the location where the Froude number is 0.357 .Figure P10.27 Pat (1) (3) (4) = 620.1 ft Z=628.3 ft x2-x =
Repeat Problem 10.27 if the Froude number is 2.75.Problem 10.27Water flows in the river shown in Fig. P10.27 with a uniform bottom slope. The total head at each section is measured by using Pitot tubes as indicated. Determine the value of \(d y / d x\) at the location where the Froude number is
Supercritical, uniform flow of water occurs in a 5.0-m-wide, rectangular, horizontal channel. The flow has a depth of \(1.5 \mathrm{~m}\) and a flow rate of \(45.0 \mathrm{~m}^{3} / \mathrm{s}\). The water flow encounters a \(0.25-\mathrm{m}\) rise in the channel bottom. Find the normal depth after
Water flows in a 5-m-wide channel with a speed of \(2 \mathrm{~m} / \mathrm{s}\) and a depth of \(1 \mathrm{~m}\). The channel bottom slopes at a rate of \(1 \mathrm{~m}\) per \(1000 \mathrm{~m}\). Determine the Manning coefficient for this channel.
The following data are taken from measurements on Indian Fork Creek: \(A=26 \mathrm{~m}^{2}, P=16 \mathrm{~m}\), and \(S_{0}=0.02 \mathrm{~m} / 62 \mathrm{~m}\). Determine the average shear stress on the wetted perimeter of this channel.
Consider laminar flow down a wide rectangular channel making an angle \(\theta\) with the horizontal. The fluid has kinematic viscosity \(v\) and the volume flow rate per unit width is given by\[ q=\frac{g y^{3} \sin \theta}{3 v} \]where \(y\) is the fluid depth perpendicular to the channel
The following data are obtained for a particular reach of the Provo River in Utah: \(A=183 \mathrm{ft}^{2}\), free-surface width \(=55 \mathrm{ft}\), average depth \(=3.3 \mathrm{ft}, R_{h}=3.32 \mathrm{ft}, V=6.56 \mathrm{ft} / \mathrm{s}\), length of reach \(=116 \mathrm{ft}\), and elevation drop
At a particular location, the cross section of the Columbia River is as indicated in Fig. P10.34. If on a day without wind it takes \(5 \mathrm{~min}\) to float 0.5 mile along the river, which drops \(0.46 \mathrm{ft}\) in that distance, determine the value of the Manning coefficient, \(n\).Figure

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