Explanation Given information: The vortex shading frequency is f k , the free stream velocity is V , the fluid density is ρ , the fluid dynamic viscosity is μ and the diameter of the cylinder is D . Expression of function of shading frequency, f k = f ( V , ρ , μ , D ) ...... (I) Dimension of density in M L T unit system, ρ = [ M L − 3 ] ...... (II) Here, the dimension of mass is M and the dimension of the length is L . Dimension of the dynamic viscosity, μ = [ M L − 1 T − 1 ] ...... (III) Here, the dimension of time is T . Dimension of free stream velocity, V = [ L T − 1 ] ...... (IV) Dimension of diameter, D = [ L ] ...... (V) Expression of vortex shading frequency, f k = ( θ t ) ...... (VI) Here, the angle is θ and the time is t . Dimension of time, t = [ T ] Dimension of angle. θ = 1 . Substitute T for t and 1 for θ in Equation ( VI). f k = ( 1 T ) = [ T − 1 ] ...... (VII) Here, the number of variable is 5 these are f k , V , ρ , μ and D and the number of dimension is 3 these are M , L and T . Expression of number of pi-terms, pi-terms = n − j ...... (VIII) Here, the number of variables is n and the number of dimensions is j . Substitute 5 for n and 3 for j in Equation (VIII). pi-terms = 5 − 3 = 2 Here, two pi-terms is present. Here, the basic variable is V , ρ and D . Expression of first pi-terms, ∏ 1 = f k V a ρ b D c ...... (IX) Here, the constants are a , b , and c . Expression of second pi-terms, ∏ 2 = μ V a ρ b D c ...... (X) Dimension of first pi-term, ∏ 1 = [ M 0 L 0 T 0 ] Dimension of second pi-term, ∏ 2 = [ M 0 L 0 T 0 ] Substitute [ M 0 L 0 T 0 ] for ∏ 1 , [ T − 1 ] for f k , [ L T − 1 ] for V , [ M L − 3 ] for ρ and [ L ] for D in Equation (IX). [ M 0 L 0 T 0 ] = [ T − 1 ] [ L T − 1 ] a [ M L − 3 ] b [ L ] c [ M 0 L 0 T 0 ] = [ M b L a − 3 b + c T − 1 − a ] ...... (XI) Compare the power of M on both sides of Equation (XI). b = 0 Compare the power of T on both sides of Equation (XI). 0 = − 1 − a a = − 1 Compare the power of L on both sides of Equation (XI) and substitute 0 for b and − 1 for a . 0 = − 1 − 3 ( 0 ) + c 0 = − 1 + c c = 1 Substitute − 1 for a , 0 for b and 1 for c in Equation (IX)

4th Edition

ISBN: 2810022150991

Author: CENGEL

Publisher: MCG

See similar textbooks

Videos

Question

Chapter 7, Problem 47P

To determine

The dimensionless relationship.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7, Problem 46P

Chapter 7, Problem 48P

Students have asked these similar questions

mylabmastering.pearson.com Chapter 12 - Lecture Notes.pptx: (MAE 272-01) (SP25) DY... P Pearson MyLab and Mastering Scores

answer the fallowing Brake Specific Fuel Consumption - 0.3 kg/kwh, Mechanical Efficiency- 90% Calorific Value of Fuel -45 MJ/kg. Given these values, find the indicated power, indicated thermal efficiency and brake thermal efficiency

Problem 6. The circular plate shown rotates about its vertical diameter. At the instant shown, the angular velocity ₁ of the plate is 10 rad/s and is decreasing at the rate of 25 rad/s². The disk lies in the XY plane and Point D of strap CD moves upward. The relative speed u of Point D of strap CD is 1.5 m/s and is decreasing at the rate of 3 m/s². Determine (a) the velocity of D, (b) the acceleration of D. Answers: =0.75 +1.299]-1.732k m/s a=-28.6 +3.03-10.67k m/s² 200 mm x Z

Chapter 7 Solutions

FLUID MECHANICS FUNDAMENTALS+APPS

Ch. 7 - What is the difference between a dimension and a...Ch. 7 - List the seven primary dimensions. What is...Ch. 7 - Write the primary dimensions of the universal...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 5P Ch. 7 - Prob. 6P Ch. 7 - Prob. 7P Ch. 7 - On a periodic chart of the elements, molar mass...Ch. 7 - Prob. 9P Ch. 7 - The moment of force(M)is formed by the cross...

Ch. 7 - You are probably familiar with Ohm law for...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 13P Ch. 7 - Thermal conductivity k is a measure of the ability...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 16P Ch. 7 - Explain the law of dimensional homogeneity in...Ch. 7 - Prob. 18P Ch. 7 - Prob. 19P Ch. 7 - An important application of fluid mechanics is the...Ch. 7 - Prob. 21P Ch. 7 - Prob. 22P Ch. 7 - In Chap. 4, we defined the material acceleration,...Ch. 7 - Newton's second law is the foundation for the...Ch. 7 - What is the primary reason for nondimensionalizing...Ch. 7 - Prob. 26P Ch. 7 - In Chap. 9, we define the stream function for...Ch. 7 - In an oscillating incompressible flow field the...Ch. 7 - Prob. 29P Ch. 7 - Consider ventilation of a well-mixed room as in...Ch. 7 - In an oscillating compressible flow field the...Ch. 7 - List the three primary purposes of dimensional...Ch. 7 - List and describe the three necessary conditions...Ch. 7 - A student team is to design a human-powered...Ch. 7 - Repeat Prob. 7-34 with all the same conditions...Ch. 7 - This is a follow-tip to Prob. 7-34. The students...Ch. 7 - The aerodynamic drag of a new sports car is lo be...Ch. 7 - This is a follow-tip to Prob. 7-37E. The...Ch. 7 - Consider the common situation in which a...Ch. 7 - Prob. 40P Ch. 7 - Some students want to visualize flow over a...Ch. 7 - A lightweight parachute is being designed for...Ch. 7 - Prob. 43P Ch. 7 - Prob. 44P Ch. 7 - Prob. 45P Ch. 7 - The Richardson number is defined as Ri=L5gV2...Ch. 7 - Prob. 47P Ch. 7 - Prob. 48P Ch. 7 - A stirrer is used to mix chemicals in a large tank...Ch. 7 - Prob. 50P Ch. 7 - Albert Einstein is pondering how to write his...Ch. 7 - Consider filly developed Couette flow-flow between...Ch. 7 - Consider developing Couette flow-the same flow as...Ch. 7 - The speed of sound c in an ideal gas is known to...Ch. 7 - Repeat Prob. 7-54, except let the speed of sound c...Ch. 7 - Repeat Prob. 7-54, except let the speed of sound c...Ch. 7 - Prob. 57P Ch. 7 - When small aerosol particles or microorganisms...Ch. 7 - Prob. 59P Ch. 7 - Prob. 60P Ch. 7 - Prob. 61P Ch. 7 - An incompressible fluid of density and viscosity ...Ch. 7 - Prob. 63P Ch. 7 - In the study of turbulent flow, turbulent viscous...Ch. 7 - Bill is working on an electrical circuit problem....Ch. 7 - A boundary layer is a thin region (usually along a...Ch. 7 - A liquid of density and viscosity is pumped at...Ch. 7 - A propeller of diameter D rotates at angular...Ch. 7 - Repeat Prob. 7-68 for the case an which the...Ch. 7 - Prob. 70P Ch. 7 - Prob. 71P Ch. 7 - Consider a liquid in a cylindrical container in...Ch. 7 - Prob. 73P Ch. 7 - One of the first things you learn in physics class...Ch. 7 - Prob. 75CP Ch. 7 - Prob. 76CP Ch. 7 - Define wind tunnel blockage. What is the rule of...Ch. 7 - Prob. 78CP Ch. 7 - Prob. 79CP Ch. 7 - In the model truck example discussed in Section...Ch. 7 - Prob. 83P Ch. 7 - A small wind tunnel in a university's...Ch. 7 - There are many established nondimensional...Ch. 7 - Prob. 86CP Ch. 7 - For each statement, choose whether the statement...Ch. 7 - Prob. 88P Ch. 7 - Prob. 89P Ch. 7 - Prob. 90P Ch. 7 - Prob. 91P Ch. 7 - From fundamental electronics, the current flowing...Ch. 7 - Prob. 93P Ch. 7 - Prob. 94P Ch. 7 - The Archimedes number listed in Table 7-5 is...Ch. 7 - Prob. 96P Ch. 7 - Prob. 97P Ch. 7 - Prob. 98P Ch. 7 - Prob. 99P Ch. 7 - Prob. 100P Ch. 7 - Repeal Prob. 7-100 except for a different...Ch. 7 - A liquid delivery system is being designed such...Ch. 7 - Prob. 103P Ch. 7 - Au aerosol particle of characteristic size DPmoves...Ch. 7 - Prob. 105P Ch. 7 - Prob. 106P Ch. 7 - Prob. 107P Ch. 7 - Prob. 108P Ch. 7 - Prob. 109P Ch. 7 - Prob. 110P Ch. 7 - Repeat pall (a) of Prob. 7-110, except instead of...Ch. 7 - Sound intensity I is defined as the acoustic power...Ch. 7 - Repeal Prob. 7-112, but with the distance r from...Ch. 7 - Engineers at MIT have developed a mechanical model...Ch. 7 - Prob. 116P Ch. 7 - Prob. 117P Ch. 7 - An electrostatic precipitator (ESP) is a device...Ch. 7 - Prob. 119P Ch. 7 - Prob. 120P Ch. 7 - Prob. 121P Ch. 7 - Prob. 122P Ch. 7 - Prob. 123P Ch. 7 - Prob. 124P Ch. 7 - The primary dimensions of kinematic viscosity are...Ch. 7 - There at four additive terms in an equation, and...Ch. 7 - Prob. 127P Ch. 7 - Prob. 128P Ch. 7 - Prob. 129P Ch. 7 - A one-third scale model of a car is to be tested...Ch. 7 - Prob. 131P Ch. 7 - A one-third scale model of an airplane is to be...Ch. 7 - Prob. 133P Ch. 7 - Prob. 134P Ch. 7 - Consider a boundary layer growing along a thin...Ch. 7 - Prob. 136P

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.

The dimensionless relationship.

Solution Summary: The author explains the dimensionless relationship between the vortex shading frequency, free stream velocity, fluid density, dynamic viscosity and diameter of the cylinder.

Videos

The dimensionless relationship.

Want to see the full answer?

Chapter 7 Solutions