A venturimeter has its axis vertical , the inlet & throat diameter being 150mm & 75mm respectively. The throat is 225mm above inlet and Cd = 0.96. Petrol of specific gravity 0.78 flows up through the meter at a rate of 0.029 m3 /sec. find the pressure difference between the inlet and throat.

 A venturimeter has its axis vertical , the inlet & throat diameter being 150mm & 75mm respectively. The throat is 225mm above inlet and Cd = 0.96. Petrol of specific gravity 0.78 flows up through the meter at a rate of 0.029 m3 /sec. find the pressure difference between the inlet and throat. 

Solution: 

 The discharge through a venturimeter is given by

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

Given: 

Cd = 0.96 

d1 =150mm= 0.015m 

d2 =75mm= 0.0075m 

a1 =(π/4)*0.0152 =0.0177m2 

a2 =(π/4)*0.00752 =0.0044m2 

Q = 0.029 m3 /sec 

By substitution, we have 

 0.029 = 0.96[0.0177*0.0044 /√( 0.01772 - 0.00442 )]*√(2*9.81*h) 

 h= 2.254m of oil 

 h= (p1/w+z1) - (p2/w + z2) 

2.254= [(p1/w)- (p2/w)]-[ z2-z1] 

2.254= [(p1/w)- (p2/w)]-[0.225] 

p1/ρg - p2/ρg =2.479 

Therefore, p1 - p2= 2.479*0.78*9810 = 18969 N/m2

 =18.969k N/m2 =18969 Pa 

Pr. Difference, p1 - p2 = 18.96 kPa