Page 121 - ebook fluid mechanics_finalize

FLUID MECHANICS

5.2.2 Shock loss at sudden contraction

Figure 5.4 : Shock Loss At Sudden Contraction

Referring to Figure 5.4, in a sudden contraction, the flow converges to form a vena

contracta at section (3) in the smaller pipe. The loss of energy in the convergence from

sections (1) to (3) is small and the main loss occurs in the enlargement from sections (3) to
(2). It is usual to ignore the loss from sections (1) to (3) and treat the loss from (3) to (2) as

if it was due to a sudden enlargement from the area of the vena contracta ac to the area a2

of the smaller pipe.

(v − v ) 2
Loss of head = C 2
2 g

For continuity of flow

a 2 v = a C v
C
2
a
If the coefficient of contraction = C = C
C
v C

a v
v = 2 2
C
a
C
1
= v
2
C C

 1  2 v 2
Loss of head at sudden contraction, hC =  − 1 2


 C c  2 g
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