Unformatted text preview: of a specific viscousflow analysis, we take the classic problem
of flow in a full pipe, driven by pressure or gravity or both. Figure 6.10 shows the
geometry of the pipe of radius R. The xaxis is taken in the flow direction and is inclined to the horizontal at an angle .
Before proceeding with a solution to the equations of motion, we can learn a lot by
making a controlvolume analysis of the flow between sections 1 and 2 in Fig. 6.10.
The continuity relation, Eq. (3.23), reduces to
Q1
or V1 Q2
Q1
A1 const
Q2
A2 V2 (6.23) since the pipe is of constant area. The steadyflow energy equation (3.71) reduces to
p1 1
2 2
1V 1 gz1 p2 1
2 2
2V 2 gz2 ghf (6.24)  v v since there are no shaftwork or heattransfer effects. Now assume that the flow is fully  eText Main Menu  Textbook Table of Contents  Study Guide 6.4 Flow in a Circular Pipe
1 p1 = p 2 + ∆ p 339 g x = g sin φ
g r= φ R r u( r) τw 2 p2 τ( r) Z1 x2 –x 1 =∆ φ L x
Z2 Fig. 6.10 Control volume of steady,
fully developed flow between two
sections in an inclined pipe. developed (Fig. 6.6), a...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.
 Spring '08
 Sakar

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