Water flows in a horizontal tube of variable cross section as shown. If the pressure difference of water between X and Y is 600 N/m2, Area of cross section of pipe at X and Y are 3 cm2 and 1.5 cm2 respectively. Find the rate of flow of water through the tube. (Assume density of water as 1000 kg/m3 and 1√10=0.316)
Given
Area of cross section
Ax=3 cm2
Ay=1.5 cm2
Change in Pressure Px−Py=600N/m2
By equation of continuity
AxVx=AyVy
VyVx=3 cm21.5 cm2=2
By Bernoulli’s equation (as the pipe is horizontal)
Px+12ρv2x=Py+12ρv2y
Px−Py=12ρ(v2y−v2x)=32ρv2x
600=32(1000)v2x
vx=2√10
vx=0.63 m/s
Rate of flow of water
Q=Ax vx=(3 cm2)(0.63 m/s)=189 cm3/s