An orifice meter with orifice diameter 10 cm is inserted in a pipe of 20 cm diameter. The pressure gauges fitted upstream and downstream of the orifice meter give reading of 19.26 N/cm2 and 9.81N/cm2 respectively. Co-efficient of discharge for the meter is given as 0.6. Find the discharge of water through pipe.

 An orifice meter with orifice diameter 10 cm is inserted in a pipe of 20 cm diameter. The pressure gauges fitted upstream and downstream of the orifice meter give reading of 19.26 N/cm2 and 9.81N/cm2 respectively. Co-efficient of discharge for the meter is given as 0.6. Find the discharge of water through pipe.

 Solution. 

Given:

 Dia. Of orifice. d0 =10 cm T

herefore area, a0 = (π102 )/4 =78.54 cm2 

 Dia. Of pipe,         d1=20 cm 

Therefore area, a0 = (π202 )/4=314.16 cm2

 p1= 19.62 N/cm2 =19.62*104N/m2 

 (p1/ρg)=(19.62*104 )/(1000*9.81) 

 =20 m of water 

Similarly         (p2/ρg)=(9.81*104 )/(1000*9.81)  

                            =10 m of water 

Therefore h=(p1/ρg)-(p2/ρg)= 20.0-10.0 

                                =10.0 m of water=1000 cm of water 

Cd=0.6 

The discharge, 

Q is given by Q=Cd*(a0a1/√a1 2 -a0 2 )*√2gh 

 =0.6*(78.54*314.16/√314.162 -78.542 )*√2*981*1000

 =68213.28 cm3 /s

 =68.21 lit./s