Page 123 - ebook fluid mechanics_finalize

FLUID MECHANICS

Example 5.2

3
A pipe carrying 0.06 m /s suddenly contracts from 200 mm to 150 mm diameter.
Assuming that the vena contracta is formed in the smaller pipe, calculate the coefficient of

contraction if the pressure head at a point upstream of the contraction is 0.655 m greater
than at a point just downstream of the vena contracta.

Solution to Example 5.2

Inserting this expression for the loss of head in Bernoulli’s equation,

2

p 1 + v 1 2 = p 2 + v 2 2 + v 2 2  1 − 1

g  2g g  2g 2g  C C 


p − p v 2   1  2  v 2

1 2 = 2 1  +  − 1  − 1


 g 2 g   C   2 g
 C 
p − p
Given, 1 2 = . 0 655
 g

Using the continuity of flow Q = Av for velocity v1 and v2.

Q
v =
1
A 1

. 0 06 4
=
 ( ) 2.0 2

1= . 91 m s /

Q
v =
2
A 2

. 0 06 4
= 3= 4 . m s /
 ( 15.0 ) 2

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