Explanation Given information: force pressure gradient = dP dx Flow : steady+ incomprssible down stream distance = x component of velocity in x-direction = u distance = h fluid viscosity = μ vertical coordinate = y In the given question, We use the method of variable to find the dimensionless quantity from the given data. Total number of parameters given, n = 5 We define the function as, Primary dimensions of all the given parameters, 1 . u = component of velocity in x-direction { u } = { velocity } { u } = { L t } { u } = { L 1 t -1 } 2 . h = distance { h } = { distance } { h } = { L } 3 . dP dx = force pressure gradient { dP dx } = { pressure distance } { dP dx } = { ML -1 t -2 distance } { dP dx } = { ML -1 t -2 L } { dP dx } = { ML -2 t -2 } 4 . μ = fluid viscosity { μ } = { mass length × time } { μ } = { M L × t } { μ } = { M Lt } { μ } = { ML -1 t -1 } 5 . y = vertical coordinate { y } = { vertical coordinate } { y } = { L } { y } = { L 1 } The number of primary dimensions is (L, M, t). Since the value of n is 5. So, J = 3, And, k = (N − J) k = (5 − 3) = 2. So, the number of pi-terms is two. For further calculation we need to choose any three repeating quantities, I choose ( h , dP dx , μ ) . Thus, by using repeating variables, first independent pi- term is formed

Fluid Mechanics: Fundamentals and Applications

4th Edition

ISBN: 9781259696534

Author: Yunus A. Cengel Dr., John M. Cimbala

Publisher: McGraw-Hill Education

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The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid stat…

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Chapter 7, Problem 96P

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The dimensional parameter generated by the given quantities.

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Chapter 7, Problem 95P

Chapter 7, Problem 97P

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Fluid Mechanics: Fundamentals and Applications

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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

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The dimensional parameter generated by the given quantities.

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Chapter 7 Solutions