Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 11, Problem 117P
To determine
The percent of reduction in the fuel consumption of the car due to the reduction of the drag coefficient.
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(b)
A 70 kg bicyclist is riding her 15 kg bicycle downhill on a road with a slope of 8°
without pedaling or braking. The bicyclist has a frontal area of 0.45 m² and a drag
coefficient of 1.1 in the upright position, and a frontal area of 0.4 m² and a drag
coefficient of 0.9 in a racing position. If the downhill speed of the bicyclist
(terminal velocity) can be determined when the total force acting on the "body" in
the direction of movement is equal to zero, determine the percentage of down
speed that she can be increased when she is in a racing position. Air temperature
is 15°C and disregarding the rolling resistance and friction at the bearing.
An airplane has a mass of 50,000 kg (without load), a wing area of 360 m2 , a maximum lift coefficient of 3.25, and a cruising drag coefficient of 0.03 at an altitude of 12,000 m. Taking the density of standard air as ρ1 = 1.225 kg/m3 at sea level and ρ2 = 0.312 kg/m3 at 12,000 m altitude.
(a) Generate a plot of the safe takeoff speed at sea level Vs the load carried by airplane (ranging from 0 kg to 20,000 kg of load).
(b) Determine the power that must be delivered by the engines for a cruising speed of 800 km/hr.
A 17,000-kg tractor-trailer rig has a frontal area of 9.2 m2, a drag coefficient of 0.96, a rolling resistance coefficient of 0.05 (multiplying the weight of a vehicle by the rolling resistance coefficient gives the rolling resistance), a bearing friction resistance of 350 N, and a maximum speed of 110 km/h on a level road during steady cruising in calm weather with an air density of 1.25 kg/m3. Now a fairing is installed to the front of the rig to suppress separation and to streamline the flow to the top surface, and the drag coefficient is reduced to 0.76. Determine the maximum speed of the rig with the fairing.
Chapter 11 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 11 - What is drag? What causes it? Why do we usually...Ch. 11 - Prob. 2CPCh. 11 - Which bicyclist is more likely to go faster: one...Ch. 11 - Prob. 4CPCh. 11 - Define the frontal area of a body subjected to...Ch. 11 - Define the planform area of a body subjected to...Ch. 11 - Prob. 7CPCh. 11 - What is the difference between streamlined and...Ch. 11 - Prob. 9CPCh. 11 - During flow over a given body, the drag force, the...
Ch. 11 - During flow over a given slender body such as a...Ch. 11 - What is terminal velocity? How is it determined?Ch. 11 - What is the difference between skin friction drag...Ch. 11 - What is the effect of surface roughness on the...Ch. 11 - Prob. 15CPCh. 11 - What is flow separation? What causes it? What is...Ch. 11 - Prob. 17CPCh. 11 - Consider laminar flow over a flat plate. How does...Ch. 11 - In general, how does the drag coefficient vary...Ch. 11 - Fairings are attached to the front and back of a...Ch. 11 - Prob. 21PCh. 11 - The resultant of the pressure and wall shear...Ch. 11 - Prob. 23PCh. 11 - Prob. 24PCh. 11 - To reduce the drag coefficient and thus to improve...Ch. 11 - A circular sign has a diameter of 50 cm and is...Ch. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - At highway speeds, about half of the power...Ch. 11 - A submarine can be treated as an ellipsoid with a...Ch. 11 - A 70-kg bicyclist is riding her 1 5-kg bicycle...Ch. 11 - A wind turbine with two or four hollow...Ch. 11 - During steady motion of a vehicle on a level road,...Ch. 11 - Prob. 37EPCh. 11 - A 0.80-m-diameter, 1 .2-rn-high garbage can is...Ch. 11 - An 8-mm-diameter plastic sphere whose density is...Ch. 11 - Prob. 40PCh. 11 - The drag coefficient of a vehicle increases when...Ch. 11 - To reduce the drag coefficient and thus to improve...Ch. 11 - During major windstorms, high vehicles such as RVs...Ch. 11 - What does the friction coefficient represent in...Ch. 11 - What fluid property is responsible for the...Ch. 11 - How is the average friction coefficient determined...Ch. 11 - Prob. 47EPCh. 11 - The local atmospheric pressure in Denver, Colorado...Ch. 11 - Prob. 50PCh. 11 - Prob. 51EPCh. 11 - Air at 25C and 1 atm is flowing over a long flat...Ch. 11 - Prob. 54PCh. 11 - During a winter day, wind at 70 km/h, 5C , and I...Ch. 11 - Prob. 56PCh. 11 - The forming section of a plastics plant puts out a...Ch. 11 - Prob. 58CPCh. 11 - Why is flow separation in flow over cylinders...Ch. 11 - Prob. 60CPCh. 11 - A 5-mm-diameter electrical transmission line is...Ch. 11 - A 1ong 5-cm-diameter steam pipe passes through...Ch. 11 - Consider 0.8-cm-diameter hail that is falling...Ch. 11 - Prob. 64EPCh. 11 - Prob. 65PCh. 11 - Prob. 66PCh. 11 - Prob. 67EPCh. 11 - One of the popular demonstrations in science...Ch. 11 - Prob. 69PCh. 11 - What is stall? What causes an airfoil to stall?...Ch. 11 - Prob. 71CPCh. 11 - Air is flowing past a symmetrical airfoil at zero...Ch. 11 - Both the lift and the drag of an airfoil increase...Ch. 11 - Prob. 74CPCh. 11 - Prob. 75CPCh. 11 - Air is flowing past a symmetrical airfoil at an...Ch. 11 - Prob. 77CPCh. 11 - Prob. 78CPCh. 11 - Prob. 79CPCh. 11 - Prob. 80CPCh. 11 - How do flaps affect the lift and the drag of...Ch. 11 - Prob. 82EPCh. 11 - Consider an aircraft that takes off at 260 km/h...Ch. 11 - Prob. 84PCh. 11 - Prob. 85PCh. 11 - A tennis ball with a mass of 57 and a diameter of...Ch. 11 - A small aircraft has a wing area of 40 m2, a lift...Ch. 11 - Prob. 89PCh. 11 - Consider a light plane that has a total weight of...Ch. 11 - A small airplane has a total mass of 1800 kg and a...Ch. 11 - An airplane has a mass of 48.000 k. a wins area of...Ch. 11 - Prob. 93EPCh. 11 - Prob. 94PCh. 11 - Prob. 95EPCh. 11 - A 2-zn-high, 4-zn-wide rectangular advertisement...Ch. 11 - 11-97 A plastic boat whose bottom surface can be...Ch. 11 - Prob. 99PCh. 11 - Prob. 100EPCh. 11 - A commercial airplane has a total mass of 150.000...Ch. 11 - Prob. 102PCh. 11 - Prob. 103PCh. 11 - Prob. 104PCh. 11 - Prob. 105PCh. 11 - Prob. 107PCh. 11 - Prob. 108PCh. 11 - Prob. 109PCh. 11 - Prob. 110PCh. 11 - Prob. 111PCh. 11 - Prob. 113PCh. 11 - Prob. 115PCh. 11 - Prob. 116PCh. 11 - Prob. 117PCh. 11 - Prob. 118PCh. 11 - Prob. 119PCh. 11 - The region of flow trailing the body where the...Ch. 11 - Prob. 121PCh. 11 - Prob. 122PCh. 11 - Prob. 123PCh. 11 - Prob. 124PCh. 11 - Prob. 125PCh. 11 - Prob. 126PCh. 11 - An airplane has a total mass of 3.000kg and a wing...Ch. 11 - Prob. 128PCh. 11 - Write a report on the history of the reduction of...Ch. 11 - Write a report oil the flips used at the leading...Ch. 11 - Discuss how to calculate drag force a unsteady...Ch. 11 - Large commercial airplanes cruise at high...Ch. 11 - Many drivers turn off their air conditioners and...Ch. 11 - Consider the boundary layer growing on a flat...
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- Bill gets a job delivering pizzas. The pizza company makes him mount a sign on the roof of his car. The frontal area of the sign is A = 0.612 ft2, and he estimates the drag coefficient to be CD = 0.94 at nearly all air speeds. Estimate how much additional money it costs Bill per year in fuel to drive with the sign on his roof compared to without the sign. Use the following additional information: He drives about 10,000 miles per year at an average speed of 45 mph. The overall car efficiency is 0.332, ? fuel = 50.2 lbm/ft3, and the heating value of the fuel is 1.53 × 107 ft . lbf/lbm. The fuel costs $3.50 per gallon. Use standard air properties. Be careful with unit conversions.arrow_forwardA 0.25 kg kite with an area of 0.65 mitres squared flies in a 25 km/h wind such that the weightless string makes an angle of 40° relative to the horizontal.The density of air is 1.22 kg/m^3.if the pull on string is 7 N.determine the lift and drag coefficient basee on the kite areaarrow_forwardAn airplane has a mass of 50,000 kg (without load), a wing area of 360 m2 , a maximum lift coefficient of 3.25, and a cruising drag coefficient of 0.03 at an altitude of 12,000 m. Taking the density of standard air as ρ1 = 1.225 kg/m3 at sea level and ρ2 = 0.312 kg/m3 at 12,000 m altitude. (a) Generate a plot on computer software ( excel, matlab, etc.) of the safe takeoff speed at sea level Vs the load carried by the airplane (ranging from 0 kg to 20,000 kg of load). (b) Determine the power that must be delivered by the engines for a cruising speed of 800 km/hr.arrow_forward
- A group of researchers from UMP conducted a project collaboration with an aircraft company to develop a small aircraft. The aircraft is designed to carry up to 2800 kg of total mass. The wing area of the aircraft is 30 m2. During takeoff, the lift coefficient of the aircraft is 0.45. Meanwhile during cruising, the drag coefficient of the aircraft is 0.035. iii. Evaluate the required power to maintain at cruising speed of 300 km/h.arrow_forwardA jet airplane weighs 160,000 N and has a zero-lift drag coefficient of 0.008 and a wing area of 42 m2. At 100 m/s at sea level, the rate of climb is 11.5 m/s. The thrust developed by the engines is equal to 27,000 N. Determine the maximum rate of climb and the corresponding flight speed at sea level . [Answer: 21.6013 m/s and 214.5577 m/s]arrow_forwardA parachute of hemi-spherical shape allows a parachute jumper of weight 90kg to descend with a steady velocity of 8 m/s ignoring air movement. The drag coefficient of parachute as determined from experiments is 1.5. Take the density of air as 1.2 kg/m³. The drag force will be equal to O 90 N O 720 N 883 N O 1156 Narrow_forward
- An airplane is cruising at a velocity of 950 km/h in air whose density is 0.526 kg/m3. The airplane has a wing planform area of 90 m2. The lift and drag coefficients on cruising conditions are estimated to be 2.0 and 0.06, respectively. The power that needs to be supplied to provide enough trust to overcome wing drag is (a) 21,500 kW (b) 19,300 kW (c) 23,600 kW (d ) 25,200 kW (e) 26,100 kWarrow_forwardThe drag coefficient for a car with a frontal area of 26 ft? is being measured in an 8 ft x 8 ft wind tunnel. The density of air under the test conditions is 2.4 x 10 3 slugs/ft, When the air flow rate is, 500,000 ft/min, the drag force on the car was measured to be 170 lb. The drag coefficient under the test conditions is most nearly O 0.30 O 0.32 O 0.28 O 0.34arrow_forwardA jet airplane weighs 160,000 N and has a zero-lift drag coefficient of 0.008 and a wing area of 42 m^2. At 100 m/s at sea level, the rate of climb is 11.5 m/s. The thrust developed by the engines is equal to 27,000 N. Determine the maximum rate of climb and the corresponding flight speed at sea level .arrow_forward
- A new car is introduced and has a drag coefficient of 0.30 and a frontal area of 1.95 sqm and is traveling at 195 km/h. How much power is required to overcome aerodynamic resistance if air density is 1.325 kg/m^3?arrow_forwardSuzy likes to drive with a silly sun ball on her car antenna. The frontal area of the ball is A = 2.08 × 10−3 m2. As gas prices rise, her husband is concerned that she is wasting fuel because of the additional drag on the ball. He runs a quick test in the wind tunnel at his university and measures the drag coefficient to be CD = 0.87 at nearly all air speeds. Estimate how many liters of fuel she wastes per year by having this ball on her antenna. Use the following additional information: She drives about 15,000 km per year at an average speed of 20.8 m/s. The overall car efficiency is 0.312, ?fuel = 0.802 kg/L, and the heating value of the fuel is 44,020 kJ/kg. Use standard air properties. Is the amount of wasted fuel significant?arrow_forwardThe car shown in the figure below moves at a constant speed on a highway and has a drag coefficient Cpc of 0.32 with the windows and roof closed. What is the percent increase of horsepower needed to maintain the speed if the windows and roof are then opened? With the windows and roof open, the drag coefficient increases to Cpo = 0.43. Assume the frontal area remains the same. Windows and roof closed: CD=CDc Windows open; roof open: C₂=CDoarrow_forward
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