Page 86 - ebook fluid mechanics_finalize

FLUID MECHANICS

Ignoring losses for horizontal meter z1 = z2

v 2 − v 2 p − p
2 1 = 1 2 ——————(1)
2g 

For continuity of flow, A v = A v , giving
1 1 2 2

A
v = 1 v
2
A 2 1

 d 2
where A =
4

Substituting in equation (1)

 A 2   p − p 
v 2  1 −1  = 2g  1 2 
1  2  
 A 2   

A   p − p  

So, v 1 = 2 )  2g  1 2 
(A 1 2 − A 2 2     

A A
Discharge, Qtheory = A 1 v = 1 2 ( gH2 ) ——————(2)
1
2
A − A 2 2
1
p − p
Where H = 1 2 = pressure difference expressed as a head of the liquid


flowing in meter venturi.

A
If area ratio, m = 1 equation (2) becomes,
A 2

2gH
Q = A
1
theory
m 2 − 1

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