A venturimeter having a diameter of 75mm at throat and 150mm dia at the enlarged end is installed in a horizontal pipeline 150mm in dia carrying an oil of specific gravity 0.9. The difference of pressure head between the enlarged end and the throat recorded by a U-tube is 175mm of mercury. Determine the discharge through the pipe. Assume the coefficient of discharge of the water as 0.97.

 A venturimeter having a diameter of 75mm at throat and 150mm dia at the enlarged end is installed in a horizontal pipeline 150mm in dia carrying an oil of specific gravity 0.9. The difference of pressure head between the enlarged end and the throat recorded by a U-tube is 175mm of mercury. Determine the discharge through the pipe. Assume the coefficient of discharge of the water as 0.97. 

Solution:

The discharge through the venturimeter is given by 

Q = Cd[a1a2 /√( a1 2 - a2 2 )]* √(2gh) 

Cd =0.97 

d1 =150mm= 0.15m 

a1 =(π/4)*0.152 = 0.0177m2 

d2 =75mm= 0.075m

 a2 = (π/4)*0.0752 = 0.0044m2 

 x= 175mm = 0.175m

 h =x[(sh/sp) -1] = 0.175[(13.6/0.9)-1] 

 = 2.469m 

by substitution, 

 Q=0.97[0.0177*0.0044 /√( 0.01772 - 0.00442 )]*√(2*9.81*2.469) 

Q= 0.03067 m3 /sec 

 = 30.67 lit/sec