To determine The relevant fluid properties and appropriate dimensionless parameters. Explanation The properties of fluid associated with the fluid is density ( ρ ) and viscosity ( μ ) . Consider that the angular velocity ( ω ) is the function of the oscillation frequency ( f ) , driving torque ( τ ) , number of paddles ( N ) , paddle height ( H ) , and paddle width ( w ) , density ( ρ ) , and viscosity ( μ ) . ( ω ) = f ( f , H , N , τ , w , ρ , μ ) (I) Here, the driving torque is τ , the oscillating frequency is f , the angular velocity is ω , the number of paddles is N , the height of the paddle is H and the width of the paddle is w . Write the dimension of the width of the paddle in F L T unit system. w = [ L ] (II) Here, the dimensions for width of paddle is L . Write the dimension of the height of the paddle in F L T unit system. H = [ L ] (III) Here, the dimensions for height of paddle is L . Write the dimension of the frequency of the paddle in F L T unit system. f = [ T − 1 ] (IV) Here, the dimensions for frequency of paddle is T − 1 . Write the expression for torque. τ = f d (V) Here, the torque is ( τ ) , the distance is d and the force is f . Substitute [ F ] for f and [ L ] for d in Equation (V). T = [ F ] × [ L ] = [ F L ] (VI) Here, the dimension for force is F and the dimension for distance is L . Write the dimension of the angular velocity of the paddle in F L T unit system. ω = [ T − 1 ] (VII) Here, the dimensions for angular velocity of paddle is T − 1 . Write the dimension of the dynamic viscosity of the fluid in F L T unit system. μ = [ F L − 2 T ] (VIII) Write the dimension of the density of the fluid in F L T unit system. ρ = [ F L − 4 T 2 ] (IX) Since, the number of paddles ( N ) is the dimensionless number. Thus, the number of variable is 7 . Write the expression for the number of pi-terms ( n ) . n = k − r (X) Here, the number of variable is k , the number of dimensions is r and the number of pi terms is n . The number of variable is 7 , the number of dimensions is 3 . Substitute 7 for k and 3 for r in Equation (X). n = 7 − 3 = 4 Write the expression for first pi terms. Π 1 = τ ρ a H b ω c (XI) Here, the constant are a , c and b . Write the expression for second pi terms. Π 2 = f ρ a H b ω c (XII) Write the expression for third pi terms. Π 3 = w ρ a H b ω c (XIII) Write the expression for fourth pi terms. Π 4 = μ ρ a H b ω c (XIV) Write the expression for relation between the pi terms. Π 1 = f ( Π 2 , Π 3 , Π 4 ) (XV) Write the dimension for pi term. Π = F 0 L 0 T 0 Conclusion: Substitute [ F L ] for τ , [ F L − 4 T 2 ] for ρ , [ L ] for H , and [ T − 1 ] for ω in Equation (XI). [ F 0 L 0 T 0 ] = [ F L ] [ F L − 4 T 2 ] a [ L ] b [ T − 1 ] c [ F 0 L 0 T 0 ] = [ F L ] [ F a L − 4 a T 2 a ] [ L b ] [ T − c ] [ F 0 L 0 T 0 ] = [ F 1 + a L 1 − 4 a + b T 2 a − c ] (XVI) Compare the exponents of F in Equation (XVI). 1 + a = 0 a = − 1 Compare the exponents of L in Equation (XVI). 1 − 4 a + b = 0 1 − 4 ( − 1 ) + b = 0 1 + 4 + b = 0 b = − 5 Compare the exponents of T in Equation (XVI). 2 a − c = 0 2 ( − 1 ) − c = 0 − 2 − c = 0 c = − 2 Substitute − 1 for a , − 5 for b , and − 2 for c in Equation (XI). Π 1 = τ ρ − 1 H − 5 ω − 2 Π 1 = τ ρ H 5 ω 2 Substitute [ T − 1 ] for f , [ F L − 4 T 2 ] for ρ , [ L ] for H , and [ T − 1 ] for ω in Equation (XII)

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

See similar textbooks

Videos

Question

Chapter 7.3, Problem 21P

To determine

The relevant fluid properties and appropriate dimensionless parameters.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.3, Problem 20P

Chapter 7.3, Problem 22P

Students have asked these similar questions

please help with this practice problem(not a graded assignment, this is a practice exam), and please explain how to use sohcahtoa

Solve this problem and show all of the work

Chapter 7 Solutions

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

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.