A pipe 200m long slopes down at 1 in 100 and tapers from 600mm diameter at the higher end to 300mm diameter at the lower end, and carries 100 lit/sec of oil (specific gravity 0.8). If the pressure gauge at the higher end reads 60 kN/m2 . Determine,

 

A pipe 200m long slopes down at 1 in 100 and tapers from 600mm diameter at the higher end to 300mm diameter at the lower end, and carries 100 lit/sec of oil (specific gravity 0.8). If the pressure gauge at the higher end reads 60 kN/m2 . Determine,

 

i. Velocities at both ends.

 ii. Pressure at the lower end. Neglect the losses

 

 Solution:

 

 Given: Length of the pipe, l= 200mm

 Diameter of the pipe at the higher end,

D1 =600mm= 0.6m, Area, A1 = (π/4)*0.62 =0.283 m2

Diameter of the pipe at the lower end,

D2 =300mm= 0.3m, Area, A2 = (π/4)*0.32 = 0.0707 m2

Height of the lower end, above datum Z2 =0

Rate of oil flow, Q=100lit/sec= 0.1 m3 /sec

Pressure at the higher end, p1 =60kN/m2

 

(i) Velocities, V1 & V2

 Now Q=A1V1 = A2V2

Where V1 & V2 are the velocities at the higher and lower side respectively.

V1= Q/A1 =0.1/0.283= 0.353m/sec

 V2= Q/A2=0.1/0.0707=1.414m/sec, and

 

 (ii) Pressure at the lower end, p2

Using Bernoulli’s equation for both ends of pipe, we have

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

60/(0.8*9.81)+0.3532 /(2*9.81)+2=p2/(0.8*9.81)+(1.4142 /2*9.81)+0

p2 /(0.8*9.81) = 9.54,

Pressure at lower end, p2 = 74.8 kN/m2