Question

Cooling water (T= 20 C) is pumped from a reservoir to rock drills on a construction job using the pipe system With Diameter D = 10 cm. The flow rate must be 130 m3/h and water must leave the spray nozzle at 30 m/s. Nozzle discharge at the 100 m above reservoir (a) Calculate the minimum pressure needed at the pump outlet. (b) Estimate the required power input if the pump efficiency is 70 percent.

know that,

K 1 = 0.1

K 2= 0.16

Joints 10 each with K joint = 0.4

Pipe D=10 cm (alumunium)

L (Total) = 250 m

Vout = 30 m/s

Answer 1

pipe dia = 10 cm = 0.1 m

flow rate in the pipe = 130 cu.m/hr

area of cross section =/2 r² = 0.00785 sq.m

velocity of water in the pipe = 130 /0.00785 = 16552 m/hr = 4.598 m/s

height of the nozzle = 100 m

velocity at the nozzle = 30 m/s

using Bernoulli's principle.

P₁ + gh₁ + /2 v₁² =  P₂ + gh₂ + /2 v₂²

pressure required to maintain the flow

P = P₁ - P₂ = g(h₂-h₁ ) + /2( v₂² - v₁² )

= 1000*9.8*100 + 1000/2 * (30² - 4.6²)

= 1,419,420‬ Pa

b) power required:

we need to pump 130 cu.m /hr

mass of water = 130000 kg to lift /hr

= 36.11 kg /s

energy required = mgh = 36.11*9.8*100 = 35389 J/s

= 35.389 kW

the pumps works at 70%

power required = 35.389/0.7 = 50.56 kW