The water is flowing through a tapering pipe having diameter 300mm and 150mm at section 1 & 2 respectively. The discharge through the pipe is 40lit/sec. the section 1 is 10m above datum and section 2 is 6m above datum. Find the intensity of pressure at section 2, if that at section 1 is 400kN/m2

 

The water is flowing through a tapering pipe having diameter 300mm and 150mm at section 1 & 2 respectively. The discharge through the pipe is 40lit/sec. the section 1 is 10m above datum and section 2 is 6m above datum. Find the intensity of pressure at section 2, if that at section 1 is 400kN/m2

Solution:

At section 1:

 

D₁=300mm=0.3m, Area a1= π/4*0.32 =0.0707m2

Pressure p₁=400kN/m2

Height of upper end above the datum, z1=10m

 

At section 2

 

D2=150mm=0.15m,

Area A₂= (π/4)*0.152 =0.01767m2

Height of lower end above the datum, z2=6m

 Rate of flow (that is discharge)

 

 Q=40lit/sec=40/1000 (1litre = 1 m3 /sec) =0.04m3 /sec

Intensity of pressure at section 2, p2 www.getmyuni.com 11

As the flow is continuous, Q = A1V1= A2V2 (Continuity equation) Therefore, V1= Q/A₁ = 0.04/0.0707 = 0.566m/sec

And                 V₂= Q/A2 = 0.04/0.01767 = 2.264m/sec

 

Apply Bernoulli’s equation at sections 1 & 2,

We get, p1/w+v1 2 /2g+z1=p2/w+v2 2 /2g+z2

 And p₂/w = p1/w + (v1 2 -v2 2 /2g) + z1-z2

                       = (400/9.81) + 1/ (2*9.81)*(0.5662 -2.2642 )+(10-6)

                       = 40.77- 0.245+4 (as w =ρ.g = 1000 x 9.81 N/m3 )

                        = 44.525m = 9.81 kN/m3

P₂ = 44.525 * w = 44.525 * 9.81 = 436.8 kN/m2