Consider laminar flow over a flat plate. The boundary layerthickness & grows with distance x down the plate and is also afunction of free-stream velocity U, fluid viscosity u, and fluiddensity p. Find the dimensionless parameters for this problem, beingsure to rearrange if necessary to agree with the standarddimensionless groups in fluid mechanics.

Solution: Mathematically, boundary layer thickness can be defined as δ=f(x,U,µ,ρ), it can be written…

Consider laminar flow over a flat plate. The boundary layer thickness & grows with distance x down the plate and is also a function of free-stream velocity U, fluid viscosity µ, and fluid density p. Find the dimensionless parameters for this problem, being sure to rearrange if necessary to agree with the standard dimensionless groups in fluid mechanics.

Consider laminar flow over a flat plate. The boundary layer thickness & grows with distance x down the plate and is also a function of free-stream velocity U, fluid viscosity µ, and fluid density p. Find the dimensionless parameters for this problem, being sure to rearrange if necessary to agree with the standard dimensionless groups in fluid mechanics.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

See similar textbooks

Similar questions

Q1: Consider laminar flow over a flat plate. The boundary layer thickness o grows with distance x down the plate and is also a function of free-stream velocity U, fluid viscosity u, and fluid density p. Find the dimensionless parameters for this problem, being sure to rearrange if neessary to agree with the standard dimensionless groups in fluid mechanics. Answer: Q2: The power input P to a centrifugal pump is assumed to be a function of the volume flow Q, impeller diameter D, rotational rate 2, and the density p and viscosity u of the fluid. Rewrite these variables as a dimensionless relationship. Hint: Take 2, p, and D as repeating variables. P e paD? = f( Answer:
During 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 .
In 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′.
- Assume the input power to a pump P (M L T-¹) is depend on Q- Flowrate (L3 T-¹), H-pump head (L), p- fluid density (ML-³) Create a relation by dimensional analysis between the power and other variables by Buckingham Theorem. Assume the input power to a pump P (M L T-¹) is depend on Q- Flowrate (L3 T-¹), H-pump head (L), p- fluid density (ML-³) Create a relation by dimensional analysis between the power and other variables by Rayleigh Method.
A liquid of density ? and viscosity ? flows by gravity through a hole of diameter d in the bottom of a tank of diameter DFig. . At the start of the experiment, the liquid surface is at height h above the bottom of the tank, as sketched. The liquid exits the tank as a jet with average velocity V straight down as also sketched. Using dimensional analysis, generate a dimensionless relationship for V as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. (Hint: There are three length scales in this problem. For consistency, choose h as your length scale.) except for a different dependent parameter, namely, the time required to empty the tank tempty. Generate a dimensionless relationship for tempty as a function of the following independent parameters: hole diameter d, tank diameter D, density ? , viscosity ? , initial liquid surface height h, and gravitational acceleration g.
Consider laminar flow through a long section of pipe, as in Fig. For laminar flow it turns out that wall roughness is not a relevant parameter unless ? is very large. The volume flow rate V· through the pipe is a function of pipe diameter D, fluid viscosity ? , and axial pressure gradient dP/dx. If pipe diameter is doubled, all else being equal, by what factor will volume flow rate increase? Use dimensional analysis.
During 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.
Ius A fluid flow situation depends on the Nelocity (V), the density several lineor dimension, 4shi, h2.pressure drep (DO > gravity (9) , Viscosity , Susface tension ). and bulk mo dulus of elasticity k. Apply dimen sional analysis. to these variables td A s*
When a capillary tube of small diameter D is inserted into a container of liquid, the liquid rises to height h inside the tube (Fig.). h is a function of liquid density ? , tube diameter D, gravitational constant g, contact angle ?, and the surface tension ?s of the liquid. (a) Generate a dimensionless relationship for h as a function of the given parameters. (b) Compare your result to the exact analytical equation for h. Are your dimensional analysis results consistent with the exact equation? Discuss.
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.
Select a common dimensionless parameter in fluid mechanics from the following: (a) angular velocity; (b) Kinematic viscosity; (c) specific volume; (d) specific weight; ( e) none of these answers
The output power W. of a spinning shaft is a function of torque T and angular velocity ? . Use dimensional analysis to express the relationship between W., T, and ? in dimensionless form. Compare your result to what you know from physics and discuss briefly