When a pipe flow suddenly expands from Aj to A2, low-speed, low-friction eddies appear in the corners and the flow gradually expands to A2 downstream. Using the suggested control volume (enclosed by the blue dashed lines) and assuming that the pressure acting on the annular ring is approximately P , show that under the assumption that the flow is incompressible the pressure downstream is P, = P¡ + pv7 (1– ) A1 A2 A2 The difference between P and P2 is pressure drop due to sudden expansion, an important pipeline design parameter.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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When a pipe flow suddenly expands from Aj to A2,
low-speed, low-friction eddies appear in the corners
and the flow gradually expands to A2 downstream.
Using the suggested control volume (enclosed by the
blue dashed lines) and assuming that the pressure
acting on the annular ring is approximately P , show
that under the assumption that the flow is
incompressible the pressure downstream is
P, = P, + pv? (1 – )
A2
A2
The difference between P and P2 is pressure drop
due to sudden expansion, an important pipeline
design parameter.
P,4V
P,, 4,,V,
Transcribed Image Text:When a pipe flow suddenly expands from Aj to A2, low-speed, low-friction eddies appear in the corners and the flow gradually expands to A2 downstream. Using the suggested control volume (enclosed by the blue dashed lines) and assuming that the pressure acting on the annular ring is approximately P , show that under the assumption that the flow is incompressible the pressure downstream is P, = P, + pv? (1 – ) A2 A2 The difference between P and P2 is pressure drop due to sudden expansion, an important pipeline design parameter. P,4V P,, 4,,V,
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