(a) Explanation Write the expression of excess pressure. Δ p l = F A (I) Here, the force is F and area is A . Write the dimension of force in F L T unit system. F = [ F ] (II) Write the dimension of area in F L T unit system. A = [ L 2 ] (III) Here, the dimension of length is L . Substitute [ F ] for F and [ L 2 ] for A in Equation (I). Δ p l = [ F ] [ L 2 ] = [ F L − 2 ] (IV) Write the dimension of diameter in F L T unit system. D = [ L ] (V) Write the dimension of velocity in F L T unit system. V 0 = [ L T − 1 ] (VI) Here, the dimension of time is T . Write the expression of frequency. ω = θ t (VII) Here, the angle is θ and the time is t . Write the dimension of angle in F L T unit system. θ = [ F 0 L 0 T 0 ] (VIII) Here, the dimension of force is F , the dimension of length is L and the dimension of time is T . Write the dimension of the time in F L T unit system. t = [ T ] (IX) Substitute [ F 0 L 0 T 0 ] for θ and [ T ] for t in Equation (VII). ω = [ F 0 L 0 T 0 ] [ T ] = [ F 0 L 0 T 0 − 1 ] = [ T − 1 ] (X) Write the dimension of dynamic viscosity in F L T unit system. μ = [ F L − 2 T ] (XI) Write the dimension of density in F L T unit system. ρ = [ F L − 4 T 2 ] (XII) Here, the number of variables is 7 these are Δ p l , D , V 0 , t , μ , ω and ρ and the number of dimension is 3 these are F , L and T . Write the expression of pi-term. pi-term = n − r (XIII) Here the number of variables is n and number of dimension is r . Substitute 7 for n and 3 for r in Equation (XIII). pi-term = 7 − 3 = 4 Here, the number of pi-terms is 4 . Consider, the basic quantity is Δ p l , D and V 0 . Write the expression of first pi-term. ∏ 1 = ρ [ Δ p l ] a [ D ] b [ V 0 ] c (IX) Here, the constants are a , b , c and d . Write the dimension of first pi-term. ∏ 1 = [ F 0 L 0 T 0 ] (X) Write the dimension of second pi-term. ∏ 2 = [ F 0 L 0 T 0 ] (XI) Write the dimension of third pi-term. ∏ 3 = [ F 0 L 0 T 0 ] (XII) Write the dimension of fourth pi-term. ∏ 4 = [ F 0 L 0 T 0 ] (XIII) Substitute [ F L − 4 T 2 ] for ρ , [ F 0 L 0 T 0 ] for ∏ 1 , [ F L − 2 ] for Δ p l , [ L ] for D and [ L T − 1 ] for V 0 in Equation (IX). [ F 0 L 0 T 0 ] = [ F L − 4 T 2 ] [ F L − 2 ] a [ L ] b [ L T − 1 ] c [ F 0 L 0 T 0 ] = [ F 1 + a L − 4 − 2 a + b + c T 2 − c ] (XIV) Compare the power of F on both sides of Equation (XIV). 0 = 1 + a a = − 1 Compare the power of T on both sides of Equation (XIV). 0 = 2 − c c = 2 Compare the power of L on both sides of Equation (XIV) and substitute − 1 for a and 2 for c . 0 = − 4 − 2 ( − 1 ) + b + ( 2 ) 0 = − 4 + 2 + b + 2 b = 0 Substitute − 1 for a , 0 for b and 2 for c in Equation (IX). ∏ 1 = ρ [ Δ p l ] − 1 [ D ] 0 [ V 0 ] 2 = ρ V 0 2 Δ p l (XV) Write the expression of second pi-term. ∏ 2 = μ [ Δ p l ] a [ D ] b [ V 0 ] c (XVI) Substitute [ F L − 2 T ] for μ , [ F 0 L 0 T 0 ] for ∏ 2 , [ F L − 2 ] for Δ p l , [ L ] for D and [ L T − 1 ] for V 0 in Equation (XVI) (b) To determine The operating frequency of model.

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Chapter 7.8, Problem 62P

(a)

To determine

The similarity requirement for the model.

The prediction equation for Δpl.

(b)

To determine

The operating frequency of model.

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Chapter 7.8, Problem 61P

Chapter 7.8, Problem 63P

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Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

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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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The similarity requirement for the model. The prediction equation for Δ p l .

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The similarity requirement for the model. The prediction equation for Δpl.

The operating frequency of model.

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Chapter 7 Solutions

The similarity requirement for the model.

The prediction equation for Δpl.