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Analysis of suddenly started laminar flow in the entrance region of a circular tube

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Abstract

Suddenly started laminar flow in the entrance region of a circular tube, with constant inlet velocity, is investigated analytically by using integral momentum approach. A closed form solution to the integral momentum equation is obtained by the method of characteristics to determine boundary layer thickness, entrance length, velocity profile, and pressure gradient.

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Abbreviations

M(ξ, τ, η):

a function

N(ξ, τ, η):

a function

p :

pressure

p*:

p/1/2ρU 2, dimensionless pressure

Q(ξ, τ, η):

a function

R :

radius of the tube

r :

radial distance

Re :

2RU/ν, Reynolds number

t :

time

U :

inlet velocity, constant for all time, uniform over the cross section

u :

velocity in the boundary layer

u*:

u/U, dimensionless velocity

u 1 :

velocity in the inviscid core

x :

axial distance

y :

distance perpendicular to the axis of the tube

y*:

y/R, dimensionless distance perpendicular to the axis

δ :

boundary layer thickness

δ*:

displacement thickness

η :

δ/R, dimensionless boundary layer thickness

θ :

momentum thickness

μ :

absolute viscosity of the fluid

ν :

μ/ρ, kinematic viscosity of the fluid

ξ :

x/(R Re), dimensionless axial distance

ρ :

density of the fluid

τ :

tU/(R Re), dimensionless time

τ w :

wall shear stress

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Authors and Affiliations

  1. Dept. of Engineering Mechanics, University of Missouri, Rolla, Missouri, USA

    X. J. R. Avula

Authors
  1. X. J. R. Avula
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Avula, X.J.R. Analysis of suddenly started laminar flow in the entrance region of a circular tube. Appl. sci. Res. 21, 248–259 (1969). https://doi.org/10.1007/BF00411611

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  • DOI: https://doi.org/10.1007/BF00411611

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