The pressure gradient AP/L in turbulent incompressible flow across a horizontal pipe with a length L is observed to be a function of pipe diameter D, fluid viscosity u and density p, fluid velocity V and pipe roughness E. Perform a dimensional analysis of the problem to find a correlation of relevant dimensionless numbers of the problem. D-diameter u- Viscosity p- Density V- Velocity E- Pipe Roughness AP/L – Pressure gradient

The pressure gradient AP/L in turbulent incompressible flow across a horizontal pipe with a length L is observed to be a function of pipe diameter D, fluid viscosity u and density p, fluid velocity V and pipe roughness E. Perform a dimensional analysis of the problem to find a correlation of relevant dimensionless numbers of the problem. D-diameter u- Viscosity p- Density V- Velocity E- Pipe Roughness AP/L – Pressure gradient

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

5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.
The time t d to drain a liquid from a hole in the bottom of atank is a function of the hole diameter d , the initial fluidvolume y 0 , the initial liquid depth h 0 , and the density ρ andviscosity μ of the fluid. Rewrite this relation as a dimensionlessfunction, using Ipsen’s method.
Consider liquid flow of density ρ , viscosity μ , and velocityU over a very small model spillway of length scale L ,such that the liquid surface tension coefficient Y is important.The quantity ρ U 2 L / Y, in this case, is important and iscalled the( a ) capillary rise, ( b ) Froude number, ( c ) Prandtl number,( d ) Weber number, ( e ) Bond number
The volume flow Q through an orifice plate is a function ofpipe diameter D , pressure drop D p across the orifice, fluiddensity ρ and viscosity μ , and orifice diameter d . Using D ,ρ , and ∆ p as r e peating variables, express this relationshipin dimensionless form.
When 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.
Dimensional analysis is to be used to correlate data on bubble size with the properties of the liquid when gas bubbles are formed by a gas issuing from a small orifice below the liquid surface. Assume that the significant variables are bubble diameter D, orifice diameter d, liquid density rho, surface tension sigma (in N/m), liquid viscosity mu, and g. Select d, rho, and g as the core variables.
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 .
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.
When 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)
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.
The thrust F of a propeller is generally thought to be afunction of its diameter D and angular velocity V , the forwardspeed V , and the density ρ and viscosity μ of the fl uid.Rewrite this relationship as a dimensionless function.
Consider steady viscous flow through a small horizontal tube. For this type of flow, the pressure gradient along the tube, Δp ⁄ ΔL should be a function of the viscosity Y, the mean velocity V, and the diameter D. By dimensional analysis, derive a func- tional relationship relating these variables. Fluid mechanics