Analyses of pitched baseballs indicate that CL of a rotating baseball is approximately

A hypothetical pressure coefficient variation over a long (length normal to the page) plate is shown. What is the coefficient of drag for the plate in this orientation and with the given pressure distribution? Assume that the reference area is the surface area (one side) of the plate.

Flow is occurring past the square rod. The pressure coefficient values are as shown. From which direction do you think the flow is coming? (a) SW direction, (b) SE direction, (c) NW direction, or (d) NE direction.

The hypothetical pressure distribution on a rod of triangular (equilateral) cross section is shown, where flow is from left to right. That is, Cp is maximum and equal to + 1.0 at the leading edge and decreases linearly to zero at the trailing edges. The pressure coefficient on the downstream face is constant with a value of - 0.5. Neglecting skin friction drag, find CD for the rod.

The pressure distribution on a rod having a triangular (equilateral) cross section is shown, where flow is from left to right. What is C0 for the rod?

Fill in the blanks for the following two statements: A. is associated with the viscous shear-stress distribution. a. Form drag b. Friction drag B. _____ is associated with the pressure distribution a. Form drag b. Friction drag.

The coefficient of drag for a body (select all that apply): a. is dimensionless b. is usually determined by experiment c. depends on thrust d. depends on the body's shape e. requires an updraft

Apply the grid method to each situation that follows. a. Use Eq. ( 11.5} on p. 409 in 11.2, to predict the drag force in newtons for an automobile that is traveling at V = 60 mph on a smnmer day. Assume that the frontal area is 2m2 , and the coefficient of drag is C0 = 0.4. b. Apply Eq. ( 11.5) on p. 409 in 11.2, to predict the speed in mph of a bicycle rider that is subject to a drag force of 5lbf on a summer's day. Assume the frontal area of the rider is A = 0.5 m2 , and the coefficient of drag is C0 = 0.3.

Using the first two sections in this chapter and using other resources, amwer the questions that follow. Strive for depth, clarity, and accuracy. Also, strive for effective use of sketches, words, and equations. a. What arc the four most important factors that influence the drag force? b. How are stress and drag related? c. What is form drag? What is friction drag?

Use information in 11.2 and 11.3 to find the coefficient of drag for each case described here. a. A sphere is falling through water, Re = 10,000. b. Air is blowing normal to a very long circular cylinder, andRe = 7,000. c. Wind is blowing normal to a billboard that is 20 ft wide by 10ft high.

If Stokes's law is considered valid below a Reynolds number of 0.5, what is the largest raindrop that will fall in accordance with Stokes's Jaw?

Determine the drag of a 2 ft X 4ft sheet of plywood held at a right angle to a stream of air (60F, 1 atm) having a velocity of35 mph.

Estimate the drag of a thin square plate (3 m by 4 m) when it is towed through water (10C). Assume a Lowing speed of about 5 m/s. a. The plate is oriented for minimum drag. b. The plate is oriented for maximum drag.

A cooling tower, used for cooling recirculating water in a modern steam power plant, is 350ft high and 200ft average diameter. Estimate the drag on the cooling tower in a 150 mph wind (T = 60F)

Estimate the ~vind force that would act on you if you were standing on top of a tower in a 30 m/s (115 ft/s) wind on a day when the temperature was 20C (68F) and the atmospheric pressure was 96 kPa (14 psia)

As shown, wind is blowing on a 55-gallon drum. Estimate the wind speed needed to tip the drum over. Work in S1 units. The mass of the drum is 48 Ibm, the diameter is 22.5 in., and the height is 34.5 in.

What drag is produced when a disk 0.75 m in diameter is submerged in water at l0C and towed behind a boat at a speed of 4 m/s? Assume orientation of the disk so that maximum drag is produced.

A circular billboard having a diameter of 7 m is mounted so as to be freely exposed to the wind. Estimate the total force exerted on the structure by a wind that has a direction normal to the structure and a speed of 50 m/s. Assume T = l0C and p = 101 kPa absolute.

Consider a large rock situated at the bottom of a river and acted on by a strong current. Estimate a typical speed of the current that will cause the rock to move downstream along the bottom of the river. List and justify all your major assumptions. Shown all calculations and work in SI units.

What is the moment at the bottom of a flagpole 20 m high and 8 em in diameter in a 37.5 m/s wind? The atmospheric pressure is 100 kPa, and the temperature is 20C.

A cylindrical anchor (vertical axis) made of concrete ('Y = 15 kN/m3 ) is reeled in at a rate of 1.0 m/s by a man in a boat. If the anchor is 30 em in diameter and 30 em long, what tension must be applied to the rope to pull it up at this rate? Neglect the weight of the rope.

A Ping-Pong ball of mass 2.6 g and diameter 38 mm is supported by an air jet. The air is at a temperature of 18C and a pressure of27 in-Hg. What is the minimum speed of the air jet?

Estimate the moment at ground level on a signpost supporting a sign measuring 3 m by 2 m if the wind is normal to the surface and has a speed of 35 m/s and the center of the sign is 4 m above the ground. Neglect the wind load on the post itself. Assume T = I 0C and p = l atm.

Windstorms sometimes blow empty boxcars off their tracks. The dimensions of one type of boxcar are shown. What minimum wind velocity normal to the side of the car would be required to blow the car over?

A semiautomatic popcorn popper is shown. After the unpopped corn is placed in screen S, the fan F blows air past the heating coils C and then past the popcorn. When the corn pops, its projected area increases; thus it is blown up and into a container. Unpopped corn has a mass of about 0.15 g per kernel and an average diameter of approximately 6 mm. When the corn pops, its average diameter is about 18 mm. Within what range of airspeeds in the chamber will the device operate properly?

Hoerner (15) presents data that show that fluttering flags of moderate-weight fabric have a drag coefficient (based on the flag area) of about 0.14. Thus the total drag is about 14 times the skin friction drag alone. Design a flagpole that is 100ft high and is to fly an American flag 6ft high. Make your own assumptions regarding other required data.

How much power is required to move a spherical-shaped submarine of diameter 1.5 m through seawater at a speed of 10 knots? Assume the submarine is fully submerged.

A blimp flies at 30 ft/s at an altitude where the specific weight of the air is 0.07 lbf/ft3 and the kinematic viscosity is l.3 X I 0-4 fr2!s. The blimp has a length-to-diameter ratio of 5 and has a drag coefficient corresponding to the streamlined body in Fig. 11.9 (on p. 413 in 1l.3 ). The diameter of the blimp is 80 ft. What is the power required to propel the blimp at this speed?

A cylindrical rod of diameter d and length L is rotated in still air about its midpoint in a horizontal plane. Assume the drag force at each section of the rod can be calculated assuming a two-dimensional flow with an oncoming velocity equal to the relative velocity component normal to the rod. Assume C1J is constant along the rod. a. Derive an expression for the average power needed to rotate the rod. b. Calculate the power for w = 50 rad/s, d = 2 em, L = 1.5 m, p = 1.2 kg/m3 , and C0 = 1.2.

Estimate the additional power (in hp) required for the truck when it is carrying the rectangular sign at a speed of 30 m/s over that required when it is traveling at the same speed but is not carrying the sign.

Estimate the added power (in hp) required for the car when the cartop carrier is used and the car is driven at I 00 km/h in a 25 km/h headwind over that required when the carrier is not used in the same conditions.

The resistance to motion of an automobile consists of rolling resistance and aerodynamic drag. The weight of an automobile is 3000 lbf, and it has a frontal area of 20 ftl. The drag coefficient is 0.30, and the coefficient of rolling friction is 0.02. Determine the percentage savings in gas mileage that one achieves when one drives at 55 mph instead of 65 mph on a level road. Assume an air temperature of 60F.

A car coasts down a very long hill. The weight of the car is 2000 lbf, and the slope of the grade is 6%. The rolling friction coefficient is 0.0 I. The frontal area of the car is 18 ft2 , and the drag coefficient is 0.29. The density of the air is 0.002 slugs /ft3. Find the maximum coasting speed of the car in mph.

An automobile with a mass of 1000 kg is driven up a hill where the slope is 3 (5.2% grade). The automobile is moving at 30 m/s. The coefficient of rolling friction is 0.02, the drag coefficient is 0.'1, and the cross-sectional area is 4 m2 . Find the power (in kW) needed for this condition. The air density is 1.2 kglm3

A bicyclist is coasting down a hill with a slope of 4 into a headwind (measured with respect to the ground) of7 m/s. The mass of the cyclist and bicycle is 80 kg, and the coefficient of rolling friction is 0.02. The drag coefficient is 0.5, and the projected area is 0.5 m2 The air density is 1.2 kglm3 . Find the speed of the bicycle in meters per second.

A bicyclist is capable of delivering 275 W of power to the wheels. How fast can the bicyclist travel in a 3 m/s headwind if his or her projected area is 0.5 m2 , the drag coefficient is 0.3, and the air density is 1.2 kglm3 ? Assume the rolling resistance is negligible.

Assume that the horsepower of the engine in the originall932 Fiat Ballilo (see Table 11.2 on p. 433 of 11 .1 0) was 40 bhp (brake horsepower) and that the maximum speed at sea level was 60 mph. Also assume that the projected area of the automobile is 30 ftl. Assume that the automobile is now fitted with a modern 220 bhp motor with a weight equal to the weight of the original motor; thus the rolling resistance is unchanged. What is the maximun1 speed of the "souped-up" Balillo at sea level?

For the truck of Prob. 11.40, assume that the total resistance is given by R = F0 + C, where Fn is the air drag and Cis the resistance due to bearing friction. If Cis constant at 350 N for the given truck, what fuel-savings percentage will be effected by the installation of the vanes when the truck travels at 100 km/h?

Suppose you are designing an object to fall through seawater with a terminal velocity of exactly 1 m/s. What variables will have the most influence on the terminal velocity? List these variables and justify your decisions.

As shown, a 35-cm-diameter emergency medicine parachute supporting a mass of 20 g is falling through air (20C). Assume a coefficient of drag of C0 = 2.2, and estimate the terminal velocity V0 Use a projected area of (-rriY)/4.

Consider a small air bubble (approximately 4 mm diameter) rising in a very tall column of liquid. Will the bubble accelerate or decelerate as it moves upward in the liquid? Will the drag of the bubble be largely skin friction or form drag? Explain.

Determine the terminal velocity in water (T = 10C) of a 8-cm baU that weighs 15 N in air.

This cube is weighted so that it will fall with one edge down as shown. The cube weighs 22.2 N in air. What will be its terminal velocity in water?

A spherical rock weighs 30 N in air and 5 N in water. Estimate its terminal velocity as it falls in water (20C).

A spherical balloon 2 m in diameter that is used for meteorological observations is filled with helium at standard conditions. The empty weight of the balloon is 3 N. What velocity of ascent will it attain under st;mdard atmospheric conditions?

A sphere 2 em in diameter rises in oil at a velocity of 1.5 cm/s. What is the specific weight of the sphere if the oil density is 900 kglm3 and the dynamic viscosity is 0.096 N s/m1 ?

A 120-lbf (534 N) skydiver is free-falling at an altitude of 6500 ft ( 1980 m). Estimate the terminal velocity in mph for minimum and maximum drag conditions. At maximum drag conditions, the product of frontal area and coefficient of drag is C0 A = 8 tr (0.743 m2 ). At mininmm drag conditions, C0 A = 1 if (0.0929 m2 ). Assume the pressure and temperature at sea level are 14.7 psia (101 kPa) and 60F (IS0 C). To calculate air properties, use the lapse rate for the U.S. standard atmosphere (see Chapter 3).

What is the terminal velocity of a 0.5-cm hailstone in air that has an atmospheric pressure of96 kPa absolute and a temperature of 0C? Assume that the hailstone has a specific weight of 6 kN/m3

A drag chute is used to decelerate an airplane after touchdown. The chute has a diameter of 12 ft and is deployed when the aircraft is moving at 200 ft/s. The mass of the aircraft is 20,000 Ibm, and the density of the air is 0.075 lbm/ft3 Find the initial deceleration of the aircraft due to the chute.

A paratrooper and parachute weigh 900 N. What rate of descent will they have if the parachute is 7 m in diameter and the air has a density of 1.20 kg/m3 ?

If a balloon weighs 0.10 N (empty) and is inflated with heliwn to a diameter of 60 em, what will be its terminal velocity in air (standard atmospheric conditions)? The helium is at standard conditions

A 2-cm plastic ball with a specific gravity of 1.2 is released from rest in water at 20C. Find the time and distance needed to achieve 99% of the terminal velocity. Write out the equation of motion by equating the mass times acceleration to the buoyant force, weight, and drag force and solve by developing a computer program or using available software. Use Eq. (11.9) on p.414 in ~11.3, for the drag coefficient. [Hint: The equation of motion can be expressed in the form dv = - (CoRe) l8f.L v + Ph - Pw dt 24 Pbd 2 Pb g where Pb is the density of the ball and Pw is the density of the water. This form avoids the problem of the drag coefficient approaching infinity when the velocity approaches zero because C0 Re/24 approaches unity as the Reynolds number approaches zero. An "if-statement" is needed to avoid a singularity in Eq. (II. 9) when the Reynolds number is zero.]

From the following list, select one topic that is interesting to you. Then, use references such as the internet to research your topic and prepare one page of written documentation that you could use to present your topic to your peers. a. Explain how an airplane works. b. Describe the aerodynamics of a flying bird. c. Explain how a propeller produces thrust. d. Explain how a kite flies.

Apply the grid method to each situation that follows. a. Usc Eq. ( 11.17), on p. 424 in 11.8, to predict the lift force in newtons for a spinning baseball. Use a coefficient of lift of CL = 1.2. 1 he speed of the baseball is 90 mph. Calculate area using A = -rrr2 , where the radius of a baseball is ,. = 1.45 in. Assume a hot summer day. b. Use Eq. (11.17), on p. 424 in 11.8, to predict the size of wing in mm2 needed for a model aircraft that has a mass of 570 g. Wing size is specified by giving the wing area (A) as viewed by an observer looking down on the wing. Assume the airplane is traveling at 80 mph on a hot summer day. Use a coefficient of lift of CL = 1.2. Assume straight and level flight so lift force balances weight.

Using 11.8 and other resources, answer the following questions. Strive for depth, clarity, and accuracy. Also, use effective sketches, words, and equations. a. What is circulation? Why is it important? b. What is lift force? c. What variables influence the magnitude of the lift force?

Analyses of pitched baseballs indicate that CL of a rotating baseball is approximately three times that shown in Fig. 11.18 (on p. 425 in 11.8). This greater CL is due to the added circulation caused by the seams of the ball. What is the lift of a ball pitched at a speed of 85 mph and with a spin rate of 35 rps? Also, how much will the ball be deflected from its original path by the time it gets to the plate as a result of the lift force? Note: lbe mound-to-plate distance is 60 ft, the weight of the baseball is 5 oz, and the circumference is 9 in. Assume standard atmospheric conditions, and assume that the axis of rotation is vertical.

As shown, a glider traveling at a constant velocity will move along a straight glide path that has an angle 6 with respect to the horiwntal. The angle 6, also called the glide ratio, is given by 6 = (C0 /CL). Use basic principles to prove the preceding statement.

A sphere of diameter 100 mm, rotating at a rate of 286 rpm, is situated in a stream of water (l5C) that has a velocity of 1.5 m/s. Determine the lift force (in newtons) on the rotating sphere.

An airplane wing having the characteristics shown in fig. 11.24 (on p. 429 in ~ 11.9) is to be designed to lift 1800 lbf when the airplane is cruising at 200 ft/s with an angle of attack of 3. If the chord length is to be 3.5 ft, what span of wing is required? Assume p = 0.0024 slugs/ftl.

A boat of the hydrofoil type has a lifting vane with an aspect ratio of 4 that has the characteristics shown in Fig. 11.24 (on. p. 429 in 11.9). 1f the angle of attack is 4 and the weight of the boat is 5 tons, what foil dimensions are needed to support the boat at a velocity of 60 fps?

One wing (wing A) is identical (same cross section) to another wing (wing B) except that wing B is twice as long as wing A. 'Ihcn for a given wind speed past both wings and with the same angle of attack, one would expect the total lift of wing B to be (a) the same as that of wing A, (b) less than that of wing A, (c) double that of wing A, or (d) more than double that of wing A.

What happens to the value of the induced drag coefficient for an aircraft that increases speed in level flight? (a) it increases, (b) it decreases, (c) it does not change.

The total drag coefficient for an airplane wing is C0 = C00 + Cf 1-rr A, where C00 is the form drag coefficient, CL is the lift coefficient and A is the aspect ratio of the wing. The power is given by P = F0 V = l/2 CoP V3 S. For level flight the lift is equal to the weight, so W/S = l/2pCL V2 , where W/S is called the "wing loading: Find an expression for V for which the power is a minimum in terms ofVMmPow

The airstream affected by the wing of an airplane can be considered to be a cylinder (stream tube) with a diameter equal to the wingspan, b. Far downstream from the wing, the tube is deflected through an angle 6 from the original direction. Apply the momentum equation to the stream tube between sections 1 and 2 and find the lift of the wing as a function of b, p, V, and e. Relating the lift to the lift coefficient, find ll as a function of b, CL, and wing area, S. Using the relation for induced drag, FL>r = F1.612, show that Cm = Cl!-rrA, where A is the wing aspect ratio.

An airplane has a rectangular-planform wing that has an elliptical spanwise lift distribution. The airplane has a mass of 1000 kg, a wing area of 16m2 , and a wingspan of 10m, and it is flying at 50 m/s at 3000 m altitude in a standard atmosphere. If the form drag coefficient is 0.0 I, calculate the total drag on the wing and the power (P = F0 V) necessary to overcome the drag.

The figure shows the relative pressure distribution for a Gottingen 387-FB lifting vane ( 19) when the angle of attack is 8. If such a vane with a 20-cm chord were used as a hydrofoil at a depth of 70 em, at what speed in l0C freshwater would cavitation begin? Also, estimate the lift per w1it of length of foil at this speed.

Consider the distribution of Cp as given for the wing section in Prob. 11.72. For this distribution of CP, the lift coefficient CL will fall within which range of values: (a) 0 < CL < 1.0; (b) 1.01 < Ct.< 2.0; (c) 2.01 < cl < 3.0; or (d) 3.0

The total drag coefficient for a wing with an elliptical lift distribution is C0 = C00 + Clt 11' A, where A is the aspect ratio. Derive an expression for CL that corresponds to mininmm C0 /CL (maximum CL/CD) and the corresponding C1./C().

A glider at 800 m altitude has a mass of 180 kg and a wing area of20 m2 The glide angle is 1.7, and the air density is 1.2 kg/m3 . If the lift coefficient of the glider is 0.83, how many minutes will it take to reach sea level on a calm day?

The wing loading on an airplane is defined as the aircraft weight divided by the wing area. An airplane with a wing loading of 2000 N/m2 has the aerodynamic characteristics given by Fig. 11.25 (on p. 431 in 11.9). Under cruise conditions the lift coefficient is 0.3. If the wing area is 10 m2 , find the drag force.

An ultralight airplane has a wing with an aspect ratio of 5 and with lift and drag coefficients corresponding to Fig. 11.24 (on p. 429 in 11.9). The planform area of the wing is 200 tr. The weight of the airplane and pilot is 400 lbf. The airplane flies at 50ft/sin air with a density of 0.002 slugs/ft3 Find the angle of attack and the drag force on the wing.

Your objective is to design a human-powered aircraft using the characteristics of the wing in Fig. 11.24 (on p. 429 in 11.9). The pilot weighs 130 pounds and is capable of outputting 1/2 horsepower (225 ft-lbf/s) of continuous power. The aircraft without the wing has a weight of 40 lbf, and the wing can be designed with a weight of0.12lbf per square foot of wing area. The drag consists of the drag of the structure plus the drag of the wing. The drag coefficient of the structure, CIXJ is 0.05, so that the total drag on the craft will be F0 = (Cv, + )~pV~S where C0 is the drag coefficient from Fig. 11.24 (on p. 429 in 11.9). The power required is equal to F0 V0 The air density is 0.00238 slugs/frl. Assess whether the airfoil is adequate, and if it is, find the optimum design (wing area and aspect ratio).