Fundamentals of Fluid Mechanics

Bruce R. Munson, Theodore H. Okiishi, Wade W. Huebsch

Chapter 9 Flow Over Immersed Bodies - all with Video Answers

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Chapter Questions

02:45

Problem 1

Assume that water flowing past the equilateral triangular bar shown in Fig. P9.1 produces the pressure distributions indicated. Determine the lift and drag on the bar and the corresponding lift and drag coefficients (based on frontal area). Neglect shear forces.

Narayan Hari

Numerade Educator

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Problem 2

Fluid flows past the two-dimensional bar shown in Fig. P9.2. The pressures on the ends of the bar are as shown, and the average shear stress on the top and bottom of the bar is $\tau_{\text {avg. }}$ Assume that the drag due to pressure is equal to the drag due to viscous effects.
(a) Determine $\tau_{\text {avg }}$ in terms of the dynamic pressure, $\rho U^{2} / 2$
(b) Determine the drag coefficient for this object.

Victor Salazar

Numerade Educator

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Problem 3

Repeat Problem 9.1 if the object is a cone (made by rotating the equilateral triangle about the horizontal axis through its
tip) rather than a triangular bar.

Victor Salazar

Numerade Educator

03:55

Problem 4

A small 15 -mm-long fish swims with a speed of $20 \mathrm{mm} / \mathrm{s}$ Would a boundary layer type flow be developed along the sides of the fish? Explain.

Prabhat Tyagi

Numerade Educator

03:43

Problem 5

The average pressure and shear stress acting on the surface of the 1 -m-square flat plate are as indicated in Fig. P9.5. Determine the lift and drag generated. Determine the lift and drag if the shear stress is neglected. Compare these two sets of results.

Narayan Hari

Numerade Educator

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Problem 6

The pressure distribution on the I-m-diameter circular disk in Fig. $P 9.6$ is given in the table. Determine the drag on the disk.

Victor Salazar

Numerade Educator

04:11

Problem 7

When you walk through still air at a rate of $1 \mathrm{m} / \mathrm{s}$, would you expect the character of the airflow around you to be most like that depicted in Fig. $9.6 \mathrm{a}, \mathrm{b}, \text { or } \mathrm{c} ? \text { Explain. (See Video } 9.3 .)$

Averell Hause

Carnegie Mellon University

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Problem 8

A .0 .10 -m-diameter circular cylinder moves through air with a speed $U$. The pressure distribution on the cylinder's surface is approximated by the three straight-line segments shown in Fig. P9.8. Determine the drag coefficient on the cylinder. Neglect shear forces.

Victor Salazar

Numerade Educator

02:01

Problem 9

Typical values of the Reynolds number for various animals moving through air or water are listed below. For which cases is inertia of the fluid important? For which cases do viscous effects dominate? For which cases would the flow be laminar; turbulent? Explain.

Dominador Tan

Numerade Educator

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Problem 10

Estimate the Reynolds numbers associated with the following objects moving through water. (a) a kayak, (b) a minnow,
(c) a submarine,
(d) a grain of sand settling to the bottom, (e) you swimming.

Victor Salazar

Numerade Educator

03:33

Problem 11

A 12 -ft-long kayak moves with a speed of $5 \mathrm{ft} / \mathrm{s}$. Would a boundary layer type flow be developed along the sides of the boat? Explain.

Prabhat Tyagi

Numerade Educator

01:01

Problem 12

Water flows past a flat plate that is oriented parallel to the flow with an upstream velocity of $0.5 \mathrm{m} / \mathrm{s}$. Determine the approximate location downstream from the leading edge where the boundary layer becomes turbulent. What is the boundary layer thickness at this location?

Narayan Hari

Numerade Educator

02:04

Problem 13

A viscous fluid flows past a flat plate such that the boundary layer thickness at a distance $1.3 \mathrm{m}$ from the leading edge is $12 \mathrm{mm}$. Determine the boundary layer thickness at distances of $0.20,2.0,$ and $20 \mathrm{m}$ from the leading edge. Assume laminar flow.

Narayan Hari

Numerade Educator

01:02

Problem 14

If the upstream velocity of the flow in Problem 9.13 is $U=1.5 \mathrm{m} / \mathrm{s},$ determine the kinematic viscosity of the fluid.

Narayan Hari

Numerade Educator

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Problem 15

Water flows past a flat plate with an upstream velocity of $U=0.02 \mathrm{m} / \mathrm{s}$. Determine the water velocity a distance of $10 \mathrm{mm}$ from the plate at distances of $x=1.5 \mathrm{m}$ and $x=15 \mathrm{m}$ from the leading edge.

Victor Salazar

Numerade Educator

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Problem 16

Approximately how fast can the wind blow past a 0.25 in.- -diameter twig if viscous effects are to be of importance throughout the entire flow field (i.e., $\operatorname{Re} < 1$ )? Explain. Repeat for a 0.004 in.- -diameter hair and a 6 -ft-diameter smokestack.

Victor Salazar

Numerade Educator

02:21

Problem 17

The typical shape of small cumulus clouds is as indicated in Fig. P9.17. Based on boundary layer ideas, explain why it is clear that the wind is blowing from right to left as indicated.

Eduard Sanchez

Numerade Educator

01:24

Problem 18

Consider flow past the flat plate described in Problem 9.15 Based on the nature of the boundary layer equations that govern this flow, Eqs. 9.8 and $9.9,$ explain why the answer to Problem 9.15 is independent of the plate length.

Dominador Tan

Numerade Educator

04:08

Problem 19

Because of the velocity deficit, $U-u,$ in the boundary layer, the streamlines for flow past a flat plate are not exactly parallel to the plate. This deviation can be determined by use of the displacement thickness, $\delta^{*}$. For air blowing past the flat plate shown in Fig. $\mathrm{P} 9.19$, plot the streamline $A-B$ that passes through the edge of the boundary layer $\left(y=\delta_{B} \text { at } x=\ell\right)$ at point $B$. That is, plot $y=y(x)$ for streamline $A-B .$ Assume laminar boundary layer flow.

Narayan Hari

Numerade Educator

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Problem 20

Air enters a square duct through a 1 -ft opening as is shown in Fig. $\mathrm{P} 9.20 .$ Because the boundary layer displacement thickness increases in the direction of flow, it is necessary to increase the cross-sectional size of the duct if a constant $U=2 \mathrm{f}$ Us velocity is to be maintained outside the boundary layer. Plot a graph of the duct size, $d,$ as a function of $x$ for $0 \leq x \leq 10$ ft if $U$ is to remain constant. Assume laminar flow.

Victor Salazar

Numerade Educator

02:33

Problem 21

A smooth, flat plate of length $\ell=6 \mathrm{m}$ and width $b=$ $4 \mathrm{m}$ is placed in water with an upstream velocity of $U=0.5 \mathrm{m} / \mathrm{s}$ Determine the boundary layer thickness and the wall shear stress at the center and the trailing edge of the plate. Assume a laminar boundary layer.

Narayan Hari

Numerade Educator

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Problem 22

An atmospheric boundary layer is formed when the wind blows over the Earth's surface. Typically, such velocity profiles can be written as a power law: $u=a y^{n},$ where the constants $a$ and $n$ depend on the roughness of the terrain. As is indicated in Fig. $P 9.22,$ typical values are $n=0.40$ for urban areas, $n=0.28$ for woodland or suburban areas, and $n=0.16$ for flat open country (Ref. 23).
(a) If the velocity is $20 \mathrm{ft} / \mathrm{s}$ at the bottom of the sail on your boat $(y=4 \mathrm{ft}),$ what is the velocity at the top of the mast $(y=30 \mathrm{ft}) ?(\mathrm{b})$ If the average velocity is $10 \mathrm{mph}$ on the tenth floor of an urban building, what is the average velocity on the sixtieth floor?

Victor Salazar

Numerade Educator

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Problem 23

A 30 -story office building (each story is 12 ft tall) is built in a suburban industrial park. Plot the dynamic pressure, $\rho u^{2} / 2,$ as a function of elevation if the wind blows at hurricane strength $(75 \mathrm{mph})$ at the top of the building. Use the atmospheric boundary layer information of Problem 9.22

Victor Salazar

Numerade Educator

04:23

Problem 24

Show that by writing the velocity in terms of the similarity variable $\eta$ and the function $f(\eta),$ the momentum equation for boundary layer flow on a flat plate (Eq. 9.9) can be written as the ordinary differential equation given by Eq. 9.14

Chai Santi

Numerade Educator

02:39

Problem 25

Integrate the Blasius equation (Eq, 9.14) numerically to determine the boundary layer profile for laminar flow past a flat plate. Compare your results with those of Table 9.1

Chai Santi

Numerade Educator

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Problem 26

An airplane flies at a speed of 400 mph at an altitude of $10,000 \mathrm{ft}$. If the boundary layers on the wing surfaces behave as those on a flat plate, estimate the extent of laminar boundary layer flow along the wing. Assume a transitional Reynolds number of $\operatorname{Re}_{\mathrm{xcr}}=5 \times 10^{5} .$ If the airplane maintains its 400 -mph speed but descends to sea-level elevation, will the portion of the wing covered by a laminar boundary layer increase or decrease compared with its value at 10,000 ft? Explain.

Victor Salazar

Numerade Educator

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Problem 27

If the boundary layer on the hood of your car behaves as one on a flat plate, estimate how far from the front edge of the hood the boundary layer becomes turbulent. How thick is the boundary layer at this location?

Victor Salazar

Numerade Educator

01:14

Problem 28

A laminar boundary layer velocity profile is approximated by $u / U=[2-(y / \delta)](y / \delta)$ for $y \leq \delta,$ and $u=U$ for $y>\delta$
(a) Show that this profile satisfies the appropriate boundary conditions.
(b) Use the momentum integral equation to determine the boundary layer thickness, $\delta=\delta(x)$

Dominador Tan

Numerade Educator

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Problem 29

A laminar boundary layer velocity profile is approximated by the two straight-line segments indicated in Fig. P9.29. Use the momentum integral equation to determine the boundary layer thickness, $\delta=\delta(x),$ and wall shear stress, $\tau_{w}=\tau_{w}(x) .$ Compare these results with those in Table 9.2

Victor Salazar

Numerade Educator

01:28

Problem 30

A laminar boundary layer velocity profile is approximated by $u / U=2(y / \delta)-2(y / \delta)^{3}+(y / \delta)^{4}$ for $y \leq \delta,$ and $u=U$ for $y>\delta$
(a) Show that this profile satisfies the appropriate boundary conditions.
(b) Use the momentum integral equation to determine the boundary layer thickness, $\delta=\delta(x)$

Dominador Tan

Numerade Educator

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Problem 31

For a fluid of specific gravity $S G=0.86$ flowing past a flat plate with an upstream velocity of $U=5 \mathrm{m} / \mathrm{s}$, the wall shear stress on the flat plate was determined to be as indicated in the table below. Use the momentum integral equation to determine the boundary layer momentum thickness, $\Theta=\Theta(x)$. Assume $\Theta=0$ at the leading edge, $x=0$

Victor Salazar

Numerade Educator

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Problem 32

Should a canoe paddle be made rough to get a "better grip on the water" for paddling purposes? Explain.

Victor Salazar

Numerade Educator

02:28

Problem 33

Two different fluids flow over two identical flat plates with the same laminar free-stream velocity. Both fluids have the same viscosity, but one is twice as dense as the other. What is the relationship between the drag forces for these two plates?

Narayan Hari

Numerade Educator

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Problem 34

Fluid flows past a flat plate with a drag force $9,$. If the free-stream velocity is doubled, will the new drag force, $\mathscr{D}_{2},$ be larger or smaller than $\mathscr{S}_{1}$ and by what amount?

Victor Salazar

Numerade Educator

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Problem 35

A model is placed in an airflow with a given velocity and then placed in water flow with the same velocity. If the drag coefficients are the same between these two cases, how do the drag forces compare between the two fluids?

Victor Salazar

Numerade Educator

01:01

Problem 36

The drag coefficient for a newly designed hybrid car is predicted to be $0.21 .$ The cross-sectional area of the car is $30 \mathrm{ft}^{2}$ Determine the aerodynamic drag on the car when it is driven through still air at $55 \mathrm{mph}$

Narayan Hari

Numerade Educator

01:02

Problem 37

A 5 -m-diameter parachute of a new design is to be used to transport a load from flight altitude to the ground with an average vertical speed of $3 \mathrm{m} / \mathrm{s}$. The total weight of the load and parachute is $200 \mathrm{N}$. Determine the approximate drag coefficient for the parachute.

Narayan Hari

Numerade Educator

02:31

Problem 38

A 50-mph wind blows against an outdoor movie screen that is $70 \mathrm{ft}$ wide and $20 \mathrm{ft}$ tall. Estimate the wind force on the screen.

Narayan Hari

Numerade Educator

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Problem 39

Two the aerodynamic drag on a car depends on the "shape" of the car. For example, the car shown in Fig. $\mathrm{P} 9.39$ has a drag $\mathrm{co}-$ efficient of 0.35 with the windows and roof closed. With the windows and roof open, the drag coefficient increases to $0.45 .$ With the windows and roof open, at what speed is the amount of power needed to overcome aerodynamic drag the same as it is at $65 \mathrm{mph}$ with the windows and roof closed? Assume the frontal area remains the same. Recall that power is force times velocity.

Victor Salazar

Numerade Educator

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Problem 40

A rider on a bike with the combined mass of $100 \mathrm{kg}$ attains a terminal speed of $15 \mathrm{m} / \mathrm{s}$ on a $12 \%$ slope. Assuming that the only forces affecting the speed are the weight and the drag, calculate the drag coefficient. The frontal area is $0.9 \mathrm{m}^{2} .$ Speculate whether the rider is in the upright or racing position.

Victor Salazar

Numerade Educator

02:11

Problem 41

A baseball is thrown by a pitcher at 95 mph through standard air. The diameter of the baseball is 2.82 in. Estimate the drag force on the baseball.

Narayan Hari

Numerade Educator

03:39

Problem 42

A logging boat is towing a log that is $2 \mathrm{m}$ in diameter and $8 \mathrm{m}$ long at $4 \mathrm{m} / \mathrm{s}$ through water. Estimate the power required if the axis of the log is parallel to the tow direction.

Prabhat Tyagi

Numerade Educator

04:00

Problem 43

A sphere of diameter $D$ and density $\rho_{s}$ falls at a steady rate through a liquid of density $\rho$ and viscosity $\mu .$ If the Reynolds number, Re $=\rho D U / \mu,$ is less than $1,$ show that the viscosity can be determined from $\mu=g D^{2}\left(\rho_{s}-\rho\right) / 18 U$

Prabhat Tyagi

Numerade Educator

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Problem 44

Determine the drag on a small circular disk of $0.01-f t$ diameter moving $0.01 \mathrm{ft} / \mathrm{s}$ through oil with a specific gravity of 0.87 and a viscosity 10,000 times that of water. The disk is oriented normal to the upstream velocity. By what percent is the drag reduced if the disk is oriented parallel to the flow?

Victor Salazar

Numerade Educator

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Problem 45

The square flat plate shown in Fig. $\mathrm{P} 9.45 a$ is cut into four equal-sized pieces and arranged as shown in Fig. $\mathrm{P} 9.45 b$, Determine the ratio of the drag on the original plate [case (a)] to the drag on the plates in the configuration shown in (b). Assume laminar boundary flow. Explain your answer physically.

Victor Salazar

Numerade Educator

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Problem 46

If the drag on one side of a flat plate parallel to the upstream flow is 9 when the upstream velocity is $U$, what will the drag be when the upstream velocity is $2 U ;$ or $U / 2 ?$ Assume laminar flow.

Victor Salazar

Numerade Educator

03:06

Problem 47

Water flows past a triangular flat plate oriented parallel to the free stream as shown in Fig. P9.47. Integrate the wall shear stress over the plate to determine the friction drag on one side of the plate. Assume laminar boundary layer flow.

Narayan Hari

Numerade Educator

01:02

Problem 48

For small Reynolds number flows, the drag coefficient of an object is given by a constant divided by the Reynolds number (see Table 9.4 . Thus, as the Reynolds number tends to zero, the drag coefficient becomes infinitely large. Does this mean that for small velocities (hence, small Reynolds numbers) the drag is very large? Explain.

Narayan Hari

Numerade Educator

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Problem 49

A rectangular cartop carrier of 1.6 -ft height, 5.0 -ft length (front to back), and 4.2 -ft width is attached to the top of a car. Estimate the additional power required to drive the car with the carrier at 60 mph through still air compared with the power required to drive only the car at $60 \mathrm{mph}$

Victor Salazar

Numerade Educator

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Problem 50

As shown in Video $\mathrm{V} 9.2$ and Fig. $\mathrm{P} 9.50 a$, a kayak is a relatively streamlined object. As a first approximation in calculating the drag on a kayak, assume that the kayak acts as if it were a smooth, flat plate $17 \mathrm{ft}$ long and $2 \mathrm{ft}$ wide. Determine the drag as a function of speed and compare your results with the measured values given in Fig. $\mathrm{P} 9.50 b$. Comment on reasons why the two sets of values may differ.

Victor Salazar

Numerade Educator

02:27

Problem 51

A three-bladed helicopter blade rotates at 200 rpm. If each blade is 12 ft long and 1.5 ft wide, estimate the torque needed to overcome the friction on the blades if they act as flat plates.

Anand Jangid

Numerade Educator

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Problem 52

A ceiling fan consists of five blades of 0.80 -m length and $0.10-\mathrm{m}$ width which rotate at $100 \mathrm{rpm} .$ Estimate the torque needed to overcome the friction on the blades if they act as flat plates.

Victor Salazar

Numerade Educator

04:10

Problem 53

A thin smooth sign is attached to the side of a truck as is indicated in Fig. $\mathrm{P} 9.53 .$ Estimate the friction drag on the sign when the truck is driven at 55 mph.

Prashant Bana

Numerade Educator

01:11

Problem 54

A 38.1 -mm-diameter, 0.0245 -N table tennis ball is released from the bottom of a swimming pool. With what velocity does it rise to the surface? Assume it has reached its terminal velocity.

Kratika Bhadauria

Numerade Educator

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Problem 55

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 $165^{\circ} \mathrm{F}$, estimate the rate at which it will rise under steady-state conditions if the atmospheric pressure is 14.7 psi.

Victor Salazar

Numerade Educator

04:59

Problem 56

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. $\mathrm{P} 9.56$ 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. Explain.

Narayan Hari

Numerade Educator

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Problem 57

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 opens. Assume that the chute opens instantly, that the drag coefficient and air density remain constant, and that the flow is quasisteady.

Victor Salazar

Numerade Educator

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Problem 58

Estimate the velocity with which you would contact the ground if you jumped from an airplane at an altitude of $5,000 \mathrm{ft}$ and
(a) air resistance is negligible,
(b) air resistance is important, but you forgot your parachute, or
(c) you use a 25 -ft-diameter parachute.

Victor Salazar

Numerade Educator

02:26

Problem 59

As is discussed in Section $9.3,$ the drag on a rough golf ball is less than that on an equal-sized smooth ball. Does it follow that
a 10 -m-diameter spherical water tank resting on a 20 -m-tall support should have a rough surface so as to reduce the moment needed at the base of the support when a wind blows? Explain.

Narayan Hari

Numerade Educator

01:07

Problem 60

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 $30 \mathrm{m} / \mathrm{s}$

Narayan Hari

Numerade Educator

03:31

Problem 61

How fast do small water droplets of $0.06-\mu \mathrm{m}$ ( $6 \times$ $10^{-8} \mathrm{m}$ ) diameter fall through the air under standard sea-level conditions? Assume the drops do not evaporate. Repeat the problem for standard conditions at $5000-\mathrm{m}$ altitude

Narayan Hari

Numerade Educator

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Problem 62

A strong wind can blow a golf ball off the tee by pivoting it about point 1 as shown in Fig. $P 9.62 .$ Determine the wind speed necessary to do this.

Victor Salazar

Numerade Educator

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Problem 63

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. (See Video $\mathrm{V} 9.14 .$ ) List any assumptions used in your calculations.

Victor Salazar

Numerade Educator

03:10

Problem 64

Determine the moment needed at the base of a $20-\mathrm{m}$ tall, 0.12 -m-diameter flag pole to keep it in place in a 20 -m/s wind.

Prabhat Tyagi

Numerade Educator

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Problem 65

Repeat Problem 9.64 if a $2-\mathrm{m}$ by 2.5 -m flag is attached to the top of the pole. See Fig. 9.30 for drag coefficient data for flags.

Victor Salazar

Numerade Educator

01:59

Problem 66

During a flash flood, water rushes over a road as shown in Fig. P9.66 with a speed of 12 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.

Narayan Hari

Numerade Educator

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Problem 67

How much more power is required to pedal a bicycle at 15 mph into a 20 -mph head-wind than at 15 mph through still air? Assume a frontal area of $3.9 \mathrm{ft}^{2}$ and a drag coefficient of $C_{D}$ $=0.88$

Victor Salazar

Numerade Educator

02:08

Problem 68

Estimate the wind velocity necessary to knock over a 20 -lb garbage can that is $3 \mathrm{ft}$ tall and $2 \mathrm{ft}$ in diameter. List your assumptions.

Narayan Hari

Numerade Educator

02:36

Problem 69

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 $A$. Would you expect your fuel consumption to be less than, equal to, or greater than $x$ gallons for this windy round-trip? Support your answer with appropriate analysis.

Narayan Hari

Numerade Educator

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Problem 70

The structure shown in Fig. P9.70 consists of three cylindrical support posts to which an elliptical flat plate sign is attached. Estimate the drag on the structure when a 50 -mph wind blows against it.

Victor Salazar

Numerade Educator

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Problem 71

A 25 -ton $(50,000-1 b)$ truck coasts down a steep $7 \%$ moun tain grade without brakes, as shown in Fig. P9.71. 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 on concrete is $1.2 \%$ of the weight and the drag coefficient based on frontal area is 0.76

Victor Salazar

Numerade Educator

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Problem 72

As shown in Video $\mathrm{V} 9.19$ and Fig. $\mathrm{P} 9.72,$ 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 mph?

Victor Salazar

Numerade Educator

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Problem 73

Which shown in Video $\mathrm{V} 9.11$ and Fig. $\mathrm{P} 9.73,$ a vertical wind tunnel can be used for skydiving practice. Estimate the vertical wind speed needed if a 150 -lb person is to be able to "float" motionless when the person (a) curls up as in a crouching position or (b) lies flat. See Fig. 9.30 for appropriate drag coefficient data.

Victor Salazar

Numerade Educator

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Problem 74

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.

Victor Salazar

Numerade Educator

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Problem 75

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 current altitude and use a standard atmosphere (see Table C.1)

Victor Salazar

Numerade Educator

02:38

Problem 76

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. $\mathrm{P} 9.76 a$
(b) as oriented in Fig. $\mathrm{P} 9.76 b$

Narayan Hari

Numerade Educator

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Problem 77

The helium-filled balloon shown in Fig $\mathrm{P} 9.77$ 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 $\theta$ as a function of $U$ for $1 \leq U \leq 50$ mph. Would this be an effective device over the range of $U$ indicated? Explain.

Victor Salazar

Numerade Educator

05:46

Problem 78

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. $\mathrm{P} 9.78$. Estimate the speed of the river current. Neglect the weight of the cable and the drag on it.

Narayan Hari

Numerade Educator

05:24

Problem 79

A shortwave radio antenna is constructed from circular tubing, as is illustrated in Fig. P9.79. Estimate the wind force on the antenna in a 100 -km/hr wind.

Narayan Hari

Numerade Educator

01:51

Problem 80

Estimate the wind force on your hand when you hold it out of your car window while driving 55 mph. Repeat your calculations if you were to hold your hand out of the window of an airplane flying 550 mph.

Narayan Hari

Numerade Educator

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Problem 81

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.

Victor Salazar

Numerade Educator

02:53

Problem 82

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 $1.03 \times 10^{-3} \mathrm{kg} / \mathrm{m}^{3} .$ If the drag coefficient at this large Mach number condition is $1.5,$ determine the deceleration of the meteor.

Narayan Hari

Numerade Educator

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Problem 83

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. $P 9.83 .$ With $U=0$ the beam is balanced. What is the minimum air velocity for which the balance arm will rotate clockwise?

Victor Salazar

Numerade Educator

01:55

Problem 84

A 2 -in.- -diameter sphere weighing 0.14 lb is suspended by the jet of air shown in Fig. $\mathrm{P} 9.84$ and Video $\mathrm{V} 3.2 .$ 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 exit.

Narayan Hari

Numerade Educator

01:38

Problem 85

A 60 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. 9.28 for drag coefficient data.

Narayan Hari

Numerade Educator

02:44

Problem 86

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 1.3 and the wind speed is a uniform $20 \mathrm{m} / \mathrm{s}$
(b) Repeat your calculations if the velocity profile against the building is a typical profile for an urban area (see Problem 9.22 ) and the wind speed halfway up the building is $20 \mathrm{m} / \mathrm{s}$.

Narayan Hari

Numerade Educator

02:46

Problem 87

A regulation football is 6.78 in. in diameter and weighs $0.91 \mathrm{lb} .$ If its drag coefficient is $C_{D}=0.2,$ determine its deceleration if it has a speed of $20 \mathrm{ft} / \mathrm{s}$ at the top of its trajectory.

Prabhat Tyagi

Numerade Educator

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Problem 88

An airplane tows a banner that is $b=0.8 \mathrm{m}$ tall and $\ell$ $=25 \mathrm{m}$ long at a speed of $150 \mathrm{km} / \mathrm{hr}$. If the drag coefficient based on the area $b \ell$ is $C_{D}=0.06,$ estimate the power required to tow the banner. Compare the drag force on the banner with that on a rigid flat plate of the same size. Which has the larger drag force and why?

Victor Salazar

Numerade Educator

02:46

Problem 89

The paint stirrer shown in Fig. $\mathrm{P} 9.89$ consists of two circular disks attached to the end of a thin rod that rotates at 80 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 power required to drive the mixer if the induced motion of the liquid is neglected.

Narayan Hari

Numerade Educator

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Problem 90

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.

Victor Salazar

Numerade Educator

03:16

Problem 91

A fishnet consists of 0.10 -in.-diameter strings tied into squares 4 in. per side. Estimate the force needed to tow a 15 -ft by 30 -ft section of this net through seawater at 5 ft/s.

Prabhat Tyagi

Numerade Educator

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Problem 92

It is suggested that the power, $9,$ needed to overcome the aerodynamic drag on a vehicle traveling at a speed $U$ varies as $\mathscr{P} \sim U^{n} .$ What is an appropriate value for the constant $n ?$ Explain.

Victor Salazar

Numerade Educator

01:40

Problem 93

Estimate the power needed to overcome the aerodynamic drag of a person who runs at a rate of 100 yds in 10 s in still air. Repeat the calculations if the race is run into a 20 -mph headwind; a 20 -mph tailwind. Explain.

Cory Kuzinski

Numerade Educator

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Problem 94

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?

Victor Salazar

Numerade Educator

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Problem 95

Two bicycle racers ride $30 \mathrm{km} / \mathrm{hr}$ through still air. By what percentage is the power required to overcome aerodynamic drag for the second cyclist reduced if she drafts closely behind the first cyclist rather than riding alongside her? Neglect any forces other than aerodynamic drag. (See Fig. 9.30 .)

Victor Salazar

Numerade Educator

02:57

Problem 96

As indicated in Fig. $\mathrm{P} 9.96,$ 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 leaf length, $L$ ) is approximated as shown. Consider a tree with leaves of length $L=0.3 \mathrm{ft}$ What wind speed will produce a drag on the tree that is 6 times greater than the drag on the tree in a $15 \mathrm{ft} / \mathrm{s}$ wind?

Narayan Hari

Numerade Educator

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Problem 97

The blimp shown in Fig. P9.97 is used at various athletic events. It is $128 \mathrm{ft}$ long and has a maximum diameter of $33 \mathrm{ft}$ If its drag coefficient (based on the frontal area) is 0.060 , estimate the power required to propel it
(a) at its 35 -mph cruising speed
(b) at its maximum 55 -mph speed.

Victor Salazar

Numerade Educator

01:45

Problem 98

If for a given vehicle it takes 20 hp to overcome aerodynamic drag while being driven at $65 \mathrm{mph}$, estimate the horsepower required at $75 \mathrm{mph}$

Narayan Hari

Numerade Educator

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Problem 99

(See Fluids in the News article "Dimpled Baseball Bats," Section 9.3.3.) 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 ball in terms of how the dimples affect the transition from a laminar to a turbulent boundary layer.

Victor Salazar

Numerade Educator

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Problem 100

(See Fluids in the News article "At $12,600 \mathrm{mpg}$ It Doesn't cost Much to 'Fill 'er Up," Section 9.3.3.) (a) Determine the power it takes to overcome aerodynamic drag on a small $\left(6 \mathrm{ft}^{2}\right.$ cross section), streamlined $\left(C_{D}=0.12\right)$ vehicle traveling $15 \mathrm{mph}$
(b) Compare the power calculated in part (a) with that for a large
$\left(36 \mathrm{ft}^{2} \text { cross-sectional area }\right),$ nonstreamlined $\left(C_{D}=0.48\right) \mathrm{SUV}$ traveling 65 mph on the interstate.

Victor Salazar

Numerade Educator

01:59

Problem 101

A rectangular wing with an aspect ratio of 6 is to generate 1000 lb of lift when it flies at a speed of $200 \mathrm{ft}$ /s. Determine the length of the wing if its lift coefficient is 1.0

Narayan Hari

Numerade Educator

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Problem 102

A $1.2-$ lb kite with an area of $6 \mathrm{ft}^{2}$ flies in a 20 -ft/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 lb, determine the lift and drag coefficients based on the kite area.

Victor Salazar

Numerade Educator

01:05

Problem 103

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.

Narayan Hari

Numerade Educator

01:39

Problem 104

A light aircraft with a wing area of $200 \mathrm{ft}^{2}$ and a weight of 2000 lb has a lift coefficient of 0.40 and a drag coefficient of
$0.05 .$ Determine the power required to maintain level flight.

Narayan Hari

Numerade Educator

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Problem 105

As shown in Video $\mathrm{V} 9.25$ and Fig. $\mathrm{P} 9.105,$ a spoiler is used on race cars to produce a negative lift, thereby giving a better tractive force. The lift coefficient for the airfoil shown is $C_{t}=1.1,$ and the coefficient of friction between the wheels and the pavement is $0.6 .$ At a speed of $200 \mathrm{mph}$, by how much would use of the spoiler increase the maximum tractive force that could be generated between the wheels and ground? Assume the airspeed past the spoiler equals the car speed and that the airfoil acts directly over the drive wheels.

Victor Salazar

Numerade Educator

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Problem 106

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.

Victor Salazar

Numerade Educator

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Problem 107

For a given airplane, compare the power to maintain level flight at a 5000 -ft altitude with that at $30,000 \mathrm{ft}$ at the same velocity. Assume $C_{D}$ remains constant.

Victor Salazar

Numerade Educator

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Problem 108

A wing generates a lift $\mathscr{L}$ when moving through sealevel 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?

Victor Salazar

Numerade Educator

04:33

Problem 109

Air blows over the flat-bottomed, two-dimensional object shown in Fig. $\mathrm{P} 9.109 .$ 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.

Narayan Hari

Numerade Educator

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Problem 110

When air flows past the airfoil shown in Fig. $\mathrm{Pg} .110$. the velocity just outside the boundary layer, $u,$ is as indicated. Estimate the lift coefficient for these conditions.

Victor Salazar

Numerade Educator