Explanation Write the functions for accuracy. A = f ( V , a , m , p , ρ , z ) (I) Here, the pressure is p , the accuracy is A , the velocity of the ball is V , the age of the pitcher is a , the density of the fluid is ρ , the mass of the pitcher is m , and the elevations above the sea level is z . Write the dimension of the distance in F L T unit system. z = [ L ] (II) Here, the dimension for distance is L . Write the dimension of the age of pitcher in F L T unit system. a = [ T ] (III) Here, the dimensions for age of pitcher is T . Write the dimension of the mass in F L T unit system. m = [ F L − 1 T 2 ] (IV) Here, the dimension for force is F , the dimension for distance is L and the time is T . Write the expression for density. ρ = m v (V) Here, the mass is m , the volume is v and the density is ρ . Substitute [ F L − 1 T 2 ] for m and [ L 3 ] for v in Equation (IV). ρ = [ F L − 1 T 2 ] [ L 3 ] = [ F L − 4 T 2 ] (VI) Here, the dimensions for force is F and the dimension for diameter is L . Write the dimension of the pressure in F L T unit system. p = [ F L − 2 ] (VII) Here, the dimensions for force is F and the dimension for diameter is L . Write the dimension of the velocity in F L T unit system. V = [ L T − 1 ] (VIII) Here, the dimensions for distance is L and the dimensions for time is T . Write the expression for the number of variable. n = k − r (IX) Here, the number of variable is k , the number of dimensions is r and the number of pi terms is n . Write the expression for first pi terms. Π 1 = A z a V b m c (X) Here, the constant are a , c and b . Write the dimension for pi term. Π = L 0 T 0 (XI) Write the expression for second pi terms. Π 2 = ρ z a V b m c c (XII) Write the expression for third pi terms. Π 3 = p z a V b m c (XIII) Write the expression for fourth pi terms. Π 4 = a z a V b m c (XIV) Write the expression for pi terms. Π 1 = f ( Π 2 , Π 3 ) (XV) Write the dimension of the accuracy in F L T unit system. A = [ F 0 L 0 T 0 ] (XVI) Conclusion: The number of variable is 7 and the number of dimensions is 3 . Substitute 7 for k and 3 for r in Equation (IX). n = 7 − 3 = 4 Substitute [ F 0 L 0 T 0 ] for A , [ F 0 L 0 T 0 ] for Π 1 , [ L T − 1 ] for V , [ L ] for z and [ F L − 1 T 2 ] for m in Equation (X). [ F 0 L 0 T 0 ] = [ F 0 L 0 T 0 ] [ L ] a [ L T − 1 ] b [ F L − 1 T 2 ] c [ F 0 L 0 T 0 ] = [ F 0 L 0 T 0 ] [ L a ] [ L b T − b ] [ F c L − c T 2 c ] [ F 0 L 0 T 0 ] = [ F c L a + b − c T 2 c − b ] (XVII) Compare the exponents of F in Equation (XVII). c = 0 (XVIII) Compare the exponents of T in Equation (XVII). 2 c − b = 0 b = 2 c (XIX) Compare the exponents of L in Equation (XVII). a + b − c = 0 (XX) Substitute 0 for c in Equation (XIX). b = 2 ( 0 ) = 0 (XXI) Substitute 0 for b and 0 for c in Equation (XX). a + 0 − 0 = 0 a = 0 (XXII) Substitute 0 for c , 0 for b and 0 for a in Equation (X). Π 1 = A z 0 V 0 m 0 = A (XXIII) Substitute [ F 0 L 0 T 0 ] for A , [ F 0 L 0 T 0 ] for Π 1 , [ L T − 1 ] for V , [ F L − 4 T 2 ] for ρ and [ F L − 1 T 2 ] for m in Equation (XII). [ F 0 L 0 T 0 ] = [ F L − 4 T 2 ] [ L ] a [ L T − 2 ] b [ F L − 4 T 2 ] c [ F 0 L 0 T 0 ] = [ F L − 4 T 2 ] [ L a ] [ L b T − 2 b ] [ F c L − 4 c T 2 c ] [ F 0 L 0 T 0 ] = [ F 1 + c L − 4 + a + b − c T 2 − b + 2 c ] (XXIV) Compare the exponents of F in Equation (XXIV)

8th Edition

ISBN: 9781119547990

Author: HOCHSTEIN

Publisher: JOHN WILEY+SONS INC.

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Chapter 7.3, Problem 26P

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Chapter 7 Solutions

EBK MUNSON, YOUNG AND OKIISHI'S FUNDAME

Ch. 7.1 - Prob. 1P Ch. 7.1 - An equation used to evaluate vacuum filtration...Ch. 7.1 - Verify the left-hand side of Eq. 7.2 is...Ch. 7.1 - The Reynolds number, ρVD/μ, is a very important...Ch. 7.1 - For the flow of a thin film of a liquid with a...Ch. 7.1 - Prob. 6P Ch. 7.3 - A mixing basin in a sewage filtration plant is...Ch. 7.3 - The excess pressure inside a bubble (discussed in...Ch. 7.3 - At a sudden contraction in a pipe the diameter...Ch. 7.3 - Water sloshes back and forth in a tank as shown in...

Ch. 7.3 - Assume that the flowrate, Q, of a gas from a...Ch. 7.3 - The pressure rise, Δp, across a pump can be...Ch. 7.3 - Prob. 13P Ch. 7.3 - Prob. 14P Ch. 7.3 - Prob. 15P Ch. 7.3 - A cone and plate viscometer consists of a cone...Ch. 7.3 - Prob. 17P Ch. 7.3 - A cylinder with a diameter D floats upright in a...Ch. 7.3 - Prob. 19P Ch. 7.3 - Prob. 20P Ch. 7.3 - Experiments are conducted on a washing machine...Ch. 7.3 - Prob. 22P Ch. 7.3 - Prob. 23P Ch. 7.3 - Prob. 24P Ch. 7.3 - Prob. 25P Ch. 7.3 - Prob. 26P Ch. 7.5 - Prob. 27P Ch. 7.5 - Prob. 28P Ch. 7.5 - Prob. 30P Ch. 7.5 - A screw propeller has the following relevant...Ch. 7.6 - Shown in the following table are several flow...Ch. 7.6 - A large, hot plate hangs vertically in a room....Ch. 7.6 - Develop the Weber number by starting with...Ch. 7.6 - Develop the Froude number by starting with...Ch. 7.6 - The following dimensionless groups are often used...Ch. 7.6 - Prob. 37P Ch. 7.7 - Prob. 38P Ch. 7.7 - The pressure drop, Δp, over a certain length of...Ch. 7.7 - Prob. 40P Ch. 7.7 - In order to maintain uniform flight, smaller birds...Ch. 7.7 - A 250-m-long ship has a wetted area of 8000 m2. A ...Ch. 7.7 - Prob. 45P Ch. 7.8 - Air at 80 °F is to flow through a 2-ft pipe at an...Ch. 7.8 - A model of a submarine, 1:15 scale, is to be...Ch. 7.8 - The drag characteristics of a torpedo are to be...Ch. 7.8 - For a certain fluid flow problem it is known that...Ch. 7.8 - The fluid dynamic characteristics of an airplane...Ch. 7.8 - If an airplane travels at a speed of 1120 km/hr at...Ch. 7.8 - (See The Wide World of Fluids article “Modeling...Ch. 7.8 - Prob. 54P Ch. 7.8 - Prob. 55P Ch. 7.8 - Prob. 56P Ch. 7.8 - Prob. 57P Ch. 7.8 - Prob. 58P Ch. 7.8 - Prob. 59P Ch. 7.8 - Prob. 60P Ch. 7.8 - Prob. 61P Ch. 7.8 - Prob. 62P Ch. 7.8 - As shown in Fig. P7.63, a “noisemaker” B is towed...Ch. 7.8 - The drag characteristics for a newly designed...Ch. 7.8 - The drag characteristics of an airplane are to be...Ch. 7.8 - The drag on a sphere moving in a fluid is known to...Ch. 7.8 - A dam spillway is 40 ft long and has fluid...Ch. 7.8 - Prob. 68P Ch. 7.8 - Prob. 69P Ch. 7.8 - Prob. 70P Ch. 7.8 - Prob. 71P Ch. 7.9 - Prob. 72P Ch. 7.9 - At a large fish hatchery the fish are reared in...Ch. 7.9 - Prob. 75P Ch. 7.9 - Prob. 76P Ch. 7.9 - Prob. 77P Ch. 7.9 - Prob. 78P Ch. 7.9 - Prob. 79P Ch. 7.9 - Prob. 80P Ch. 7.9 - Prob. 81P Ch. 7.9 - Prob. 82P Ch. 7.10 - Prob. 83P Ch. 7.10 - Prob. 84P Ch. 7.10 - Prob. 85P Ch. 7.10 - Prob. 86P Ch. 7.10 - Prob. 87P Ch. 7.10 - Prob. 88P Ch. 7.11 - Prob. 1LLP Ch. 7.11 - Prob. 2LLP

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