Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Question
Chapter 7, Problem 106P
To determine
The relationships between the four dimensionless parameters mentioned in the question and focus on Stanton number.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A stirrer is used to mix chemicals in a large tank. The shaft power W . supplied to the stirrer blades is a function of stirrer diameter D, liquid density ? ,liquidviscosity ? , and the angular velocity ? of the spinning blades.Use the method of repeating variables to generate a dimensionless relationship between these parameters. Show all your work and be sure to identify your Π groups, modifying them as necessary.
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.
A stirrer is used to mix chemicals in a tank let tank diameter Dtank and average liquid depth htank. The shaft power W . supplied to the stirrer blades is a function of stirrer diameter D, liquid density ? ,liquidviscosity ? , and the angular velocity ? of the spinning blades.Use the method of repeating variables to generate a dimensionless relationship between these parameters. Show all your work and be sure to identify your Π groups, modifying them as necessary.
Chapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
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. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - On a periodic chart of the elements, molar mass...Ch. 7 - Prob. 9PCh. 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. 13PCh. 7 - Thermal conductivity k is a measure of the ability...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 16PCh. 7 - Explain the law of dimensional homogeneity in...Ch. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - An important application of fluid mechanics is the...Ch. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 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. 26PCh. 7 - In Chap. 9, we define the stream function for...Ch. 7 - In an oscillating incompressible flow field the...Ch. 7 - Prob. 29PCh. 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. 40PCh. 7 - Some students want to visualize flow over a...Ch. 7 - A lightweight parachute is being designed for...Ch. 7 - Prob. 43PCh. 7 - Prob. 44PCh. 7 - Prob. 45PCh. 7 - The Richardson number is defined as Ri=L5gV2...Ch. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - A stirrer is used to mix chemicals in a large tank...Ch. 7 - Prob. 50PCh. 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. 57PCh. 7 - When small aerosol particles or microorganisms...Ch. 7 - Prob. 59PCh. 7 - Prob. 60PCh. 7 - Prob. 61PCh. 7 - An incompressible fluid of density and viscosity ...Ch. 7 - Prob. 63PCh. 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. 70PCh. 7 - Prob. 71PCh. 7 - Consider a liquid in a cylindrical container in...Ch. 7 - Prob. 73PCh. 7 - One of the first things you learn in physics class...Ch. 7 - Prob. 75CPCh. 7 - Prob. 76CPCh. 7 - Define wind tunnel blockage. What is the rule of...Ch. 7 - Prob. 78CPCh. 7 - Prob. 79CPCh. 7 - In the model truck example discussed in Section...Ch. 7 - Prob. 83PCh. 7 - A small wind tunnel in a university's...Ch. 7 - There are many established nondimensional...Ch. 7 - Prob. 86CPCh. 7 - For each statement, choose whether the statement...Ch. 7 - Prob. 88PCh. 7 - Prob. 89PCh. 7 - Prob. 90PCh. 7 - Prob. 91PCh. 7 - From fundamental electronics, the current flowing...Ch. 7 - Prob. 93PCh. 7 - Prob. 94PCh. 7 - The Archimedes number listed in Table 7-5 is...Ch. 7 - Prob. 96PCh. 7 - Prob. 97PCh. 7 - Prob. 98PCh. 7 - Prob. 99PCh. 7 - Prob. 100PCh. 7 - Repeal Prob. 7-100 except for a different...Ch. 7 - A liquid delivery system is being designed such...Ch. 7 - Prob. 103PCh. 7 - Au aerosol particle of characteristic size DPmoves...Ch. 7 - Prob. 105PCh. 7 - Prob. 106PCh. 7 - Prob. 107PCh. 7 - Prob. 108PCh. 7 - Prob. 109PCh. 7 - Prob. 110PCh. 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. 116PCh. 7 - Prob. 117PCh. 7 - An electrostatic precipitator (ESP) is a device...Ch. 7 - Prob. 119PCh. 7 - Prob. 120PCh. 7 - Prob. 121PCh. 7 - Prob. 122PCh. 7 - Prob. 123PCh. 7 - Prob. 124PCh. 7 - The primary dimensions of kinematic viscosity are...Ch. 7 - There at four additive terms in an equation, and...Ch. 7 - Prob. 127PCh. 7 - Prob. 128PCh. 7 - Prob. 129PCh. 7 - A one-third scale model of a car is to be tested...Ch. 7 - Prob. 131PCh. 7 - A one-third scale model of an airplane is to be...Ch. 7 - Prob. 133PCh. 7 - Prob. 134PCh. 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.Similar questions
- Dimensional analysis can be used in problems other than áuid mechanics ones. The important variablesaffecting the period of a vibrating beam (usually designated as T and with dimensions of time) are the beamlength `, area moment of inertia I, modulus of elasticity E, material density , and Poissonís ratio , so thatT = f cn(`; I; E; ; )Recall that the modulus of elasticity has typical units of N/m2 and Poissonís ratio is dimensionless.(a) Find dimensionless version of the functional relationship.(b) If E and I must always appear together (meaning that EI is e§ectively a single variable), Önd a dimensionless version of the functional relationship.arrow_forwardThe spin rate of a tennis ball determines the aerodynamic forces acting on it. In turn, the spin rate is a§ectedby the aerodynamic torque. If the torque depends on áight speed V , density , viscosity , ball diameter D,angular velocity !, and the fuzz height, hf , Önd the important dimensionless variables for this case. Use V ,, and D as your scaling (repeating) variables.arrow_forwardIn the study of turbulent flow, turbulent viscous dissipation rate ? (rate of energy loss per unit mass) is known to be a function of length scale l and velocity scale u′ of the large-scale turbulent eddies. Using dimensional analysis (Buckingham pi and the method of repeating variables) and showing all of your work, generate an expression for ? as a function of l and u′.arrow_forward
- Consider fully developed flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary. The flow is steady, incompressible, and two-dimensional in the xy-plane. a) Use the first principle (dimensional analysis) to generate a dimensionless relationship for the x-component of fluid velocity u as a function of fluid viscosity μ, top plate speed v, distance h, fluid density ρ, and distance y. b) Name the common dimensionless number formed in (a). Hint: modifying the dimensionless number if necessary.arrow_forwardThe drag coefficient in aircraft industry affected by some parameters which are thespeed of plane (v), the plane length (L), the air density (ρ), the air dynamic viscosity(μ), and speed of sound (a). By using dimensional analysis, identify two non-dimensionnumbers in which the drag coefficient is a function of them and explain how these twowill effect on drag coefficient.arrow_forwardWhen fluid in a pipe is accelerated linearly from rest, it begins as laminar flow andthen undergoes transition to turbulence at a time ttr which depends upon the pipe diameter D,fluid acceleration a, density ρ, and viscosity µ. Arrange this into a dimensionless relationbetween ttr and D. (Fluid Mechanics)arrow_forward
- In making a dimensional analysis, what rules do you followfor choosing your scaling variables?arrow_forwardDuring World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumedthat the energy released E , was a function of blast waveradius R , air density ρ, and time t . Arrange these variablesinto a single dimensionless group, which we may term theblast wave number .arrow_forwardWrite the primary dimensions of each of the following variables from the field of thermodynamics, showing all your work: (a) energy E; (b) specific energy e = E/m; (c) power W . .arrow_forward
- The Stokes-Oseen formula for drag force on a sphere at low speed is given asD = 3dV +916V 2d2, where D is drag, V is velocity, is density, d is the sphere diameter, and is the viscosity coe¢ cient.(a) Using the formula given, Önd the dimensions of the viscosity coe¢ cient. (Donít simply look upthe dimensions; use the formula to show them.) Be sure to show your work. Find the primaryunits of viscosity in SI and British units.(b) Verify that the Stokes-Oseen formula is dimensionally homogeneous.arrow_forwardThere are many common dimensionless numbers used to describedifferent physical effects. Such dimensionless numbers are usually a ratioof specific properties, for example, the Reynolds number represents theratio of inertial to viscous forces.Choose three of the following dimensionless numbers and describe whatproperties the ratio represents and the context in which these numbers areimportant: Froude Number, Euler Number, Mach Number, Weber Number,Nusselt Number, Prandtl Number.arrow_forwardthe differential equation for conservation of mass, the continuity equation. In cylindrical coordinates, and for steady flow, 1/ r ∂(rur) /∂r + 1/ r ∂u? /∂? + ∂uz /∂z = 0 Write the primary dimensions of each additive term in the equation, and verify that the equation is dimensionally homogeneous. Show all your work.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Unit Conversion the Easy Way (Dimensional Analysis); Author: ketzbook;https://www.youtube.com/watch?v=HRe1mire4Gc;License: Standard YouTube License, CC-BY