Explanation Write the expression for thickness function. h = f ( l , ρ , g , σ ) (I) Here, length is l , density of material is ρ , acceleration due to gravity is g and surface tension is σ . Write the expression for dimension of thickness. h = [ L ] (II) Here, dimension of thickness is [ L ] . Write the expression for density. ρ = m V (III) Here, mass is m volume is V . Substitute [ M ] for dimension of m and [ L 3 ] for dimension of V in Equation (III) ρ = [ M ] [ L 3 ] = [ M L − 3 ] (IV) Here, dimension of mass is [ M ] . Write the expression for dimension of acceleration due to gravity. g = [ L T − 2 ] (V) Here, dimension of time is [ T ] . Write the expression for surface tension. σ = F l (VI) Here, force is F , length is l . Substitute [ M L T − 2 ] for dimension of F and [ L ] for dimension of l in Equation (VI) σ = [ M L T − 2 ] [ L ] = [ M T − 2 ] (VII) Write the expression for dimension of length.. l = [ L ] (VIII) Write the expression for number of dimensionless numbers or pi terms. Π = n − r (IX) Here, number of variable is n and reference dimension is r . Substitute 5 for n and 3 for r in Equation (IX). Π = 5 − 3 = 2 (X) Here, number of pi terms is 2 . Write the expression for dimensionless first pi terms using repeating variable and dependent variable. Π 1 = h ( l ) a ( g ) b ( ρ ) c (XI) Here, constants are a , b and c . Write the expression for second pi terms using non-repeating variable and dependent variable. Π 2 = σ ( l ) p ( g ) q ( ρ ) r (XII) Here, constant are p , q , and r . Write the expression for first pi-terms as a function of second pi-terms. Π 1 = f ( Π 2 ) (XIII) Substitute the dimension [ L ] for h , [ L ] for l , [ M L − 3 ] for ρ , [ L T − 2 ] for g and [ M 0 L 0 T 0 ] for Π 1 in Equation (IX) [ M 0 L 0 T 0 ] = [ L ] [ L ] a [ L T − 2 ] b [ M L − 3 ] c [ M 0 L 0 T 0 ] = [ M ] c [ L ] a − 2 b − 3 c + 1 [ T ] − 2 b (XIV) Compare exponent of [ M ] to obtain c in Equation (XIV)

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ISBN: 9781119547990

Author: HOCHSTEIN

Publisher: JOHN WILEY+SONS INC.

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Chapter 7.3, Problem 14P

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The suitable set of dimensionless parameters.

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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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