A horizontal venturimeter with inlet diameter 20cm and throat diameter 10cm is used to measure the flow of water. The pressure at inlet is 17.658 N/cm2 and the vacuum pressure at the throat is 30cm of mercury. Find the discharge of water through venturimeter. Take Cd=0.98

 A horizontal venturimeter with inlet diameter 20cm and throat diameter 10cm is used to measure the flow of water. The pressure at inlet is 17.658 N/cm2 and the vacuum pressure at the throat is 30cm of mercury. Find the discharge of water through venturimeter. Take Cd=0.98 

Solution: 

Dia at inlet, d1=20cm 

                         a1=(πd1 2 )/4=(π202 )/4=314.16cm2 

 Dia at throat,d2=10cm a

                          2=(π102 )/4=78.54cm2 

p1=17.658 N/cm2 =17.658*104N/m2 

density of water = 1000kg/m3 and 

Therefore, p1/ρg=17.658*104 /9.81*1000=18m of water 

 p2/ρg= -30cm of mercury (vacuum pr. Head) 

 = - 0.30m of mercury 

 = - 0.30*13.6 

 = - 4.08 m of water 

Therefore differential head 

 h= p1/ρg - p2/ρg =18-(-4.08) 

 = 18+4.08=22.08 m of water = 2208 cm of water 

 

The discharge Q is given by equation

 Q= Cd*(a1a2/(√a1 2 -a2 2 ))*(√2gh)

 =0.98*(314.16*78.54/(√314.162 78.542 ))*(√2*9.81*2208) 

 =50328837.21/304 

 =1655555 cm3 /s 

 Q =165.55 lit/s