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Unformatted text preview: of a specific viscous-flow 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 x-axis 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 control-volume analysis of the flow between sections 1 and 2 in Fig. 6.10.
The continuity relation, Eq. (3.23), reduces to
or V1 Q2
A2 V2 (6.23) since the pipe is of constant area. The steady-flow energy equation (3.71) reduces to
1V 1 gz1 p2 1
2V 2 gz2 ghf (6.24) | v v since there are no shaft-work or heat-transfer effects. Now assume that the flow is fully | e-Text 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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- Spring '08