A pipe through which the water is flowing, is having diameters 20 cm and 10 cm at the crosssections 1 and 2 respectively. The velocity of water at section 1 is given 40m/s. find the velocity head at sections 1 and 2, and also rate of discharge.

 

A pipe through which the water is flowing, is having diameters 20 cm and 10 cm at the crosssections 1 and 2 respectively. The velocity of water at section 1 is given 40m/s. find the velocity head at sections 1 and 2, and also rate of discharge.

Solution

D1=20 cm =0.2m,

A1=π/4 x D1 2 = 0.0314 m2 ,

v1=4 m/s

 D2=0.1m,

A₂=π/4 x D2 2 = 0.00785 m2

Velocity head at section 1

V₁ ² / 2g = 4 x4 /2x9.81=0.815 m

Velocity head at section 2 = V₂ 2 /2g

To find V2, apply continuity equation at sections 1&2

A₁V₁=A2V2

V₂= A₂V₂/A₂= 0.0314 x4/0.00785 =16.0 m/s

 Velocity head at sec.2 = V₂ ² /2g = 16 x16 /2 x9.81

V₂ = 83.047 m

Rate of discharge = A₁V₁ or A₂V₂= 0.0314 x 4

 =0.1256 m3/s

 = 125.6 lit/s [1 m3 = 1000litres]