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
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