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engineering
engineering fluid mechanics
Questions and Answers of
Engineering Fluid Mechanics
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
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
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} /
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
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
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} /
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.
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
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
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
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?
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
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
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
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
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
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.
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
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)
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
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
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
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
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
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
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
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}
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
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
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
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
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
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
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
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
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
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
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 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
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 \(\left(6 \mathrm{ft}^{2}\right.\)
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
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
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
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
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
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
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),
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
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
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.
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
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,
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
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
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
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.
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}
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
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
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
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
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
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
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
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
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
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
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
(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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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 \(1000 \mathrm{~m}\).
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
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\[
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
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
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