Fluid Mechanics Fundamentals And Applications
3rd Edition
ISBN: 9780073380322
Author: Yunus Cengel, John Cimbala
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 7, Problem 87P
To determine
The expression showing relationship between Froude Number and Reynolds Number
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Please solve this problem, Thank you very much! Figure is attached
1. liquids in rotating cylinders rotates as a rigid body and considered at rest. The elevation difference h between the center of the liquid surface and the rim of the liquid surface is a function of angular velocity ?, fluid density ?, gravitational acceleration ?, and radius ?. Use the method of repeating variables to find a dimensionless relationship between the parameters. Show all the steps.
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Use Buckingham's PI Theorem to determine non-dimensional
parameters in the phenomenon shown on the right (surface tension of
a soap bubble). The variables involved are:
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AP - pressure difference between the inside and outside
R- radius of the bubble
Pide
Soap
film
surface tension
(Gravity is not relevant since the soap bubble is neutrally buoyant in air)
How can I use dimensional analysis to show that in this problem both Froude's number and Reynold's number are relevant dimensionless parameters?
Problem:
Here shallow waves move at speed c. The surface of the waves is a function depth (h), gravitational accelaration is g, densisty is p and fluid viscosity is μ. I need to get the parameter in the form in the image.
Please help :)
Chapter 7 Solutions
Fluid Mechanics Fundamentals And Applications
Ch. 7 - List the seven primary dimensions. What is...Ch. 7 - What is the difference between a dimension and a...Ch. 7 - Write the primary dimensions of the universal...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - On a periodic chart of the elements, molar mass...Ch. 7 - Prob. 8PCh. 7 - Prob. 9PCh. 7 - The moment of force(M)is formed by the cross...
Ch. 7 - Prob. 11PCh. 7 - You are probably familiar with Ohm law for...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 14PCh. 7 - Prob. 15PCh. 7 - Thermal conductivity k is a measure of the ability...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 18PCh. 7 - Prob. 19EPCh. 7 - Explain the law of dimensional homogeneity in...Ch. 7 - In Chap. 4, we defined the material acceleration,...Ch. 7 - Newton's second law is the foundation for the...Ch. 7 - Prob. 23PCh. 7 - Prob. 24PCh. 7 - An important application of fluid mechanics is the...Ch. 7 - Prob. 26PCh. 7 - Prob. 27PCh. 7 - What is the primary reason for nondimensionalizing...Ch. 7 - Prob. 29PCh. 7 - In an oscillating compressible flow field the...Ch. 7 - In Chap. 9, we define the stream function for...Ch. 7 - In an oscillating incompressible flow field the...Ch. 7 - Prob. 33PCh. 7 - Consider ventilation of a well-mixed room as in...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 - A lightweight parachute is being designed for...Ch. 7 - Prob. 41PCh. 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 - Some students want to visualize flow over a...Ch. 7 - Prob. 46PCh. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - A stirrer is used to mix chemicals in a large tank...Ch. 7 - Prob. 52PCh. 7 - Albert Einstein is pondering how to write his...Ch. 7 - The Richardson number is defined as Ri=L5gV2...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. 60PCh. 7 - When small aerosol particles or microorganisms...Ch. 7 - Prob. 62PCh. 7 - Prob. 63PCh. 7 - Prob. 64PCh. 7 - An incompressible fluid of density and viscosity ...Ch. 7 - Prob. 66PCh. 7 - One of the first things you learn in physics class...Ch. 7 - Prob. 68PCh. 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 - In the study of turbulent flow, turbulent viscous...Ch. 7 - Prob. 75PCh. 7 - Consider a liquid in a cylindrical container in...Ch. 7 - Prob. 77PCh. 7 - Prob. 78CPCh. 7 - Prob. 79CPCh. 7 - Prob. 80CPCh. 7 - Define wind tunnel blockage. What is the rule of...Ch. 7 - Prob. 82CPCh. 7 - In the model truck example discussed in Section...Ch. 7 - A small wind tunnel in a university's...Ch. 7 - Prob. 87PCh. 7 - There are many established nondimensional...Ch. 7 - Prob. 89CPCh. 7 - For each statement, choose whether the statement...Ch. 7 - Prob. 91PCh. 7 - Prob. 92PCh. 7 - Prob. 93PCh. 7 - The Archimedes number listed in Table 7-5 is...Ch. 7 - Prob. 95PCh. 7 - Prob. 96PCh. 7 - Prob. 98PCh. 7 - Prob. 99PCh. 7 - Repeal Prob. 7-100 except for a different...Ch. 7 - Prob. 101PCh. 7 - Prob. 102PCh. 7 - Au aerosol particle of characteristic size DPmoves...Ch. 7 - Prob. 104PCh. 7 - Prob. 105PCh. 7 - Prob. 106PCh. 7 - Prob. 107PCh. 7 - Prob. 108PCh. 7 - Prob. 109PCh. 7 - Prob. 110PCh. 7 - An electrostatic precipitator (ESP) is a device...Ch. 7 - Prob. 113PCh. 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. 118PCh. 7 - Prob. 119PCh. 7 - Prob. 120PCh. 7 - Prob. 121PCh. 7 - The primary dimensions of kinematic viscosity are...Ch. 7 - Prob. 123PCh. 7 - Prob. 124PCh. 7 - Prob. 125PCh. 7 - There at four additive terms in an equation, and...Ch. 7 - Prob. 127PCh. 7 - Prob. 128PCh. 7 - Prob. 129PCh. 7 - Which similarity condition is related to...Ch. 7 - A one-third scale model of a car is to be tested...Ch. 7 - A one-fourth scale model of a car is to be tested...Ch. 7 - A one-third scale model of an airplane is to be...Ch. 7 - Prob. 134PCh. 7 - Prob. 135PCh. 7 - Prob. 136PCh. 7 - Consider a boundary layer growing along a thin...Ch. 7 - Prob. 138P
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- I want handwritten don't copy from chegg same to same change it even if u copy and handwritten onlyarrow_forwardQ4: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr = and the Reynolds number (Re pch. are relevant dimensionless parameters Fr = f (Re). The wave speed c of %3D waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density p, and fluid viscosity u. P. u Figure 1arrow_forwardEvaluate the use of dimensionless analysis using the Buckingham Pi Theorem for a given fluid flow system (D4) , where resistance tomotion ‘R’ for a sphere of diameter ‘D’ moving at constant velocity on the surface of a liquid is due to the density ‘ρ’ and the surfacewaves produced by the acceleration of gravity ‘g’. The dimensionless quantity linking these quantities is Ne= Function (Fr). To do thisyou must apply dimensional analysis to fluid flow system given in Figure 1 (P11). PICTURE IS ALSO ATTACHEDarrow_forward
- I need the answer as soon as possiblearrow_forwardDuring World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumed that the energy released E, was a function of blastwave radius R, air density ρ, and time t. Arrange these variables into single dimensionless group, which we mayterm the blast wave number.arrow_forward7-67 A liquid of density p and viscosity u is pumped at volume flow rate b through a pump of diameter D. The blades of the pump rotate at angular velocity w. The pump supplies a pressure rise AP to the liquid. Using dimensional analysis, generate a dimensionless relationship for AP as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. Hint: For consistency (and whenever possible), it is wise to choose a length, a density, and a velocity (or angular velocity) as repeating variables.arrow_forward
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- Hi, Please help me with this question and show the full solution,. Thank you very mucharrow_forward3- Use dimensional analysis to show that in a problem involving shallow water waves, both the Froude number and the Reynolds number are relevant dimensionless parameters. The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g. fluid density p, and fluid viscosity μ. Manipulate your's to get the parameters into the following form: Fr= √=f(Re) where Re=pch μ h Too 8 P₂ μarrow_forwardWhen a liquid in a beaker is stired, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (@) of the whirlpool, fluid density (p). gravitational acceleration (2), and radius (R) of the container. Take o. pand R as the repeating variables.arrow_forward
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