Fluid Mechanics
8th Edition
ISBN: 9781259165924
Author: Frank White
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 5, Problem 5.12P
The Stokes number, St, used in particle dynamics studies, is a dimensionless combination of five variables: acceleration of gravity g, viscosity
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The Stokes number, St, used in particle dynamics studies,is a dimensionless combination of five variables: accelerationof gravity g , viscosity μ , density ρ , particle velocity U ,and particle diameter D . ( a ) If St is proportional to μand inversely proportional to g , find its form . ( b ) Showthat St is actually the quotient of two more traditionaldimensionless groups.
The Stokes number, St, used in particle-dynamics studies is a dimensionless combination of 5 variables: acceleration of gravity g, viscosity μ, density p, particle velocity U, and particle diameter D. If St is propotional to μ and inversely proportional to g, find its dimensionless form.
The thrust force of propeller (P) depends upon the flow velocity V, angular velocity o, diameter D, dynamic viscosity , density p. the speed of sound in the medium C. (1) Derive the relationship between the above variables and the thrust force by using Buckingham's IT-theorem. (2) Explain the physical meaning of the obtained dimensionless groups.
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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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- If you disturb a tank of length L and water depth h , thesurface will oscillate back and forth at frequency Ω ,assumed here to depend also upon water density ρ and theacceleration of gravity g . ( a ) Rewrite this as a dimensionlessfunction. ( b ) If a tank of water sloshes at 2.0 Hz onearth, how fast would it oscillate on Mars ( g ≈ 3.7 m/s 2 )?arrow_forwardA simply supported beam of diameter D , length L , and modulusof elasticity E is subjected to a fluid crossflow of velocityV , density ρ , and viscosity μ . Its center deflection δ isassumed to be a function of all these variables. ( a ) Rewritethis proposed function in dimensionless form. ( b ) Suppose itis known that δ is independent of μ , inversely proportionalto E , and dependent only on ρ V 2 , not ρ and V separately.Simplify the dimensionless function accordingly. Hint:Take L , ρ , and V as r e peating variables.arrow_forwardIn supersonic wind tunnel testing, if different gases areused, dynamic similarity requires that the model and prototypehave the same Mach number and the same( a ) Euler number, ( b ) speed of sound, ( c ) stagnation enthalpy,( d ) Froude number, ( e ) specific-heat ratioarrow_forward
- The thrust F of a propeller is generally thought to be afunction of its diameter D and angular velocity V , the forwardspeed V , and the density ρ and viscosity μ of the fl uid.Rewrite this relationship as a dimensionless function.arrow_forwardA simply supported beam of diameter D, length L, and modulus of elasticity E is subjected to a fluid crossflow of velocity V, density p, and viscosity u. Its center deflection & is assumed to be a function of all these variables. Part A-Rewrite this proposed function in dimensionless form.arrow_forwardConsider the following equation. All three of the terms in parentheses are dimensionless groups. Because kC is difficult to determine directly, the other variables are measured and kC is calculated from the given equation. What is the estimated value of kC? What are the units of kC? Show your work. The following values were measured: D = 8.0 mm, DAB = 0.475 cm2/s, μ = 1.12 x 10–3 N-s/m2, ρ = 1.00 x 10–3 g/cm3, v = 15.0 m/s. Note: Given Equation attached belowarrow_forward
- During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumedthat the energy released E , was a function of blast waveradius R , air density ρ, and time t . Arrange these variablesinto a single dimensionless group, which we may term theblast wave number .arrow_forwardHow can I use dimensional analysis to show that in this problem both Froude's number and Reynold's number are relevant dimensionless parameters? Problem: Here shallow waves move at speed c. The surface of the waves is a function depth (h), gravitational accelaration is g, densisty is p and fluid viscosity is μ. I need to get the parameter in the form in the image. Please help :)arrow_forwardDuring World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumed that the energy released E, was a function of blastwave radius R, air density ρ, and time t. Arrange these variables into single dimensionless group, which we mayterm the blast wave number.arrow_forward
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