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2 and 2 U RDR Ry XV U M M 2 P RDR: 2 R y y y X y Ry R Ry

The document provides instructions for developing a momentum integral equation to analyze steady flow without blowing or suction in the entry region of a circular tube. It notes the typical terms that would be used in the momentum equation and expressions for normal stress, shear stress, and boundary conditions. The procedure from pages 42-43 of another source is to be followed.

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Santosa Edy Wibowo
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42 views1 page

2 and 2 U RDR Ry XV U M M 2 P RDR: 2 R y y y X y Ry R Ry

The document provides instructions for developing a momentum integral equation to analyze steady flow without blowing or suction in the entry region of a circular tube. It notes the typical terms that would be used in the momentum equation and expressions for normal stress, shear stress, and boundary conditions. The procedure from pages 42-43 of another source is to be followed.

Uploaded by

Santosa Edy Wibowo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Solutions Manual - Chapter 5

Convective Heat and Mass Transfer, 4th Ed., Kays, Crawford, and Weigand rev 092004

5-1

Develop a momentum integral equation for steady flow without blowing or suction for use in the
entry region of a circular tube. Note that Eq. (5-4) is not applicable for this case because it has been
assumed that the boundary-layer thickness is small relative to the body radius R; in the present case
the boundary layer ultimately grows to the centerline of the tube.
Let r = R be the wall and r = y be the edge of the control volume where the velocity becomes the inviscid
core velocity of the developing flow. Typical terms would be
R
Mx 2 u 2 rdr and My (R y)2 xv y y uy
R y

R
Normal stress = P 2 rdr
R y

Shear stress : s 2 R x; y 2 (R y) x

Now follow the procedure on pages 42-43,

1 d R 2 ucore d R y ducore
s
u rdr urdr u core
y 1
R dx R y R dx R y 2 R dx

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