Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 5, Problem 5.82P
A one-fiftieth-scale model of a military airplane is tested at 1020 m/s in a wind tunnel at sea-level conditions. The model wing area is 180 cm2. The angle of attack is 3°. If the measured model lift is 860 N, what is the prototype lift, using Mach number scaling, when it flies at 10,000 m standard altitude under dynamically similar conditions? Note: Be careful with the area scaling.
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Q1: The drag on a 2m-diameter satellite dish due to an 80 km/hr wind is to be determined
through a water tunnel test using a geometrically similar 0.25m-diameter model dish.
(a) At what water speed should the model test be run?
(b) With all similarity conditions satisfied, the measured drag on the model was determined to be
200 N. What is the predicted drag on the prototype dish?
(c) What is the Mach number, Ma = u/a where a is the speed of sound, for the prototype air flow
and the one in the water tunnel?
PS: The kinematic viscosity of air is 1.56 x10-5 m²/s.-The kinematic viscosity of water is 1.0 x10-
6 m²/s. The speed of sound is 340 m/s in air and 1500 m/s in water.
A one-tenth-scale model of a supersonic wing tested at 700 m/sin air at 20 ° C and 1 atm shows a pitching moment of 0.25kN ? m. If Reynolds number effects are negligible, what willthe pitching moment of the prototype wing be if it is flying atthe same Mach number at 8-km standard altitude?
A wind tunnel is used to measure the pressure distribution in the airflow over an airplane model. The air speed in the wind tunnel is low enough that compressible effects are negligible. The Bernoulli equation approximation is valid in such a flow situation everywhere except very close to the body surface or wind tunnel wall surfaces and in the wake region behind the model. Far away from the model, the air flows at speed V∞ and pressure P∞, and the air density ? is approximately constant. Gravitational effects are generally negligible in airflows, so we write the Bernoulli equation asP + 1/2 ρV2 = P∞ + 1/2 ρV2∞ Nondimensionalize the equation, and generate an expression for the pressure coefficient Cp at any point in the flow where the Bernoulli equation is valid. Cp is defined as Cp = P−P∞/1/2ρV2
Chapter 5 Solutions
Fluid Mechanics
Ch. 5 - Prob. 5.1PCh. 5 - A prototype automobile is designed for cold...Ch. 5 - P5.3 The transfer of energy by viscous dissipation...Ch. 5 - When tested in water at 20°C flowing at 2 m/s, an...Ch. 5 - P5.5 An automobile has a characteristic length and...Ch. 5 - P5.6 The disk-gap-band parachute in the...Ch. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - The Richardson number, Ri, which correlates the...Ch. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - The Stokes number, St, used in particle dynamics...Ch. 5 - Prob. 5.13PCh. 5 - Flow in a pipe is often measured with an orifice...Ch. 5 - The wall shear stress T in a boundary layer is...Ch. 5 - P5.16 Convection heat transfer data are often...Ch. 5 - If you disturb a tank of length L and water depth...Ch. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - As will be discussed in Chap. 11, the power P...Ch. 5 - The period T of vibration of a beam is a function...Ch. 5 - Prob. 5.24PCh. 5 - The thrust F of a propeller is generally thought...Ch. 5 - A pendulum has an oscillation period T which is...Ch. 5 - Prob. 5.27PCh. 5 - Prob. 5.28PCh. 5 - P5.29 When fluid in a pipe is accelerated linearly...Ch. 5 - Prob. 5.30PCh. 5 - P5.31 The pressure drop per unit length in...Ch. 5 - A weir is an obstruction in a channel flow that...Ch. 5 - Prob. 5.33PCh. 5 - Prob. 5.34PCh. 5 - Prob. 5.35PCh. 5 - Prob. 5.36PCh. 5 - Prob. 5.37PCh. 5 - Prob. 5.38PCh. 5 - Prob. 5.39PCh. 5 - Prob. 5.40PCh. 5 - A certain axial flow turbine has an output torque...Ch. 5 - When disturbed, a floating buoy will bob up and...Ch. 5 - Prob. 5.43PCh. 5 - Prob. 5.44PCh. 5 - P5.45 A model differential equation, for chemical...Ch. 5 - P5.46 If a vertical wall at temperature Tw is...Ch. 5 - The differential equation for small-amplitude...Ch. 5 - Prob. 5.48PCh. 5 - P5.48 A smooth steel (SG = 7.86) sphere is...Ch. 5 - Prob. 5.50PCh. 5 - Prob. 5.51PCh. 5 - Prob. 5.52PCh. 5 - Prob. 5.53PCh. 5 - Prob. 5.54PCh. 5 - Prob. 5.55PCh. 5 - P5.56 Flow past a long cylinder of square...Ch. 5 - Prob. 5.57PCh. 5 - Prob. 5.58PCh. 5 - Prob. 5.59PCh. 5 - Prob. 5.60PCh. 5 - Prob. 5.61PCh. 5 - Prob. 5.62PCh. 5 - The Keystone Pipeline in the Chapter 6 opener...Ch. 5 - Prob. 5.64PCh. 5 - Prob. 5.65PCh. 5 - Prob. 5.66PCh. 5 - Prob. 5.67PCh. 5 - For the rotating-cylinder function of Prob. P5.20,...Ch. 5 - Prob. 5.69PCh. 5 - Prob. 5.70PCh. 5 - The pressure drop in a venturi meter (Fig. P3.128)...Ch. 5 - Prob. 5.72PCh. 5 - Prob. 5.73PCh. 5 - Prob. 5.74PCh. 5 - Prob. 5.75PCh. 5 - Prob. 5.76PCh. 5 - Prob. 5.77PCh. 5 - Prob. 5.78PCh. 5 - Prob. 5.79PCh. 5 - Prob. 5.80PCh. 5 - Prob. 5.81PCh. 5 - A one-fiftieth-scale model of a military airplane...Ch. 5 - Prob. 5.83PCh. 5 - Prob. 5.84PCh. 5 - *P5.85 As shown in Example 5.3, pump performance...Ch. 5 - Prob. 5.86PCh. 5 - Prob. 5.87PCh. 5 - Prob. 5.88PCh. 5 - P5.89 Wall friction Tw, for turbulent flow at...Ch. 5 - Prob. 5.90PCh. 5 - Prob. 5.91PCh. 5 - Prob. 5.1WPCh. 5 - Prob. 5.2WPCh. 5 - Prob. 5.3WPCh. 5 - Prob. 5.4WPCh. 5 - Prob. 5.5WPCh. 5 - Prob. 5.6WPCh. 5 - Prob. 5.7WPCh. 5 - Prob. 5.8WPCh. 5 - Prob. 5.9WPCh. 5 - Prob. 5.10WPCh. 5 - Given the parameters U,L,g,, that affect a certain...Ch. 5 - Prob. 5.2FEEPCh. 5 - Prob. 5.3FEEPCh. 5 - Prob. 5.4FEEPCh. 5 - Prob. 5.5FEEPCh. 5 - Prob. 5.6FEEPCh. 5 - Prob. 5.7FEEPCh. 5 - Prob. 5.8FEEPCh. 5 - In supersonic wind tunnel testing, if different...Ch. 5 - Prob. 5.10FEEPCh. 5 - Prob. 5.11FEEPCh. 5 - Prob. 5.12FEEPCh. 5 - Prob. 5.1CPCh. 5 - Prob. 5.2CPCh. 5 - Prob. 5.3CPCh. 5 - Prob. 5.4CPCh. 5 - Does an automobile radio antenna vibrate in...Ch. 5 - Prob. 5.1DPCh. 5 - Prob. 5.2DP
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- (b) A wind-tunnel experiment is performed on a small 1:5 linear-scale model of a car, in order to assess the drag force F on a new full-size car design. A dimensionless "drag coefficient" Ca is defined by C, =- pu'A where A is the maximum cross-sectional area of the car in the flow. With the model car, a force of 3 N was recorded at a flow velocity u of 6 m s. Assuming that flow conditions are comparable (i.e., at the same Reynolds number), calculate the expected drag force for the full-sized car when the flow velocity past it is 31 m s (equivalent to 70 miles per hour). [The density of air p= 1.2 kg m.]arrow_forward(e) An airplane flies at 800km/h at 11700m standard altitude where the ambient pressure and temperature are 20.335 kPA and 216.66K respectively. A 1/50 scale model of the airplane is tested in a wind tunnel where the temperature is 288K. Calculate the tunnel test section wind speed and pressure such that force coefficients of the model and prototype are the same. Assume viscosity is proportional to the square root of T. [ Hint: flow is viscous and compressible; equation of state for a perfect gas applies]arrow_forward2 A prototype car is designed for cold weather operation in Denver (-10°C, 83 kPa, altitude 1600m, µ = 1.741 × 10-5 Pas). It's drag force is to be tested in a 1:7 model in a wind tunnel at 150 mph under standard sea level conditions. If the model and prototype satisfy dynamic similarity what prototype velocity, in mph, is matched? Is this a reasonable test? 1 mile = 1609 m HINT: p = pRTarrow_forward
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