An airlift raises 001 m3s of water from a well 100 m deep th

An air-lift raises 0.01 m^3/s of water from a well 100 m deep through a 100 mm diameter pipe. The level of the water is 40 m below the surface. The air consumed is 0.1 m^3/s of free air compressed to 800 kN/m^2. Calculate the efficiency of the pump and the mean velocity of the mixture in the pipe. The mean pressure is 345 KN/m^2

Solution

For water lifiting, work done = rho*g*Q*H

= 1000*9.81*0.01*(100+40)

= 13734 Watts = 13.734 kW

Input energy = P*Q = 800*0.1 = 80 kW

Efficiency = 13.734 / 80

= 0.1717 or 17.17%

Cross-section area of pipe = 3.14/4 * 0.1² = 0.00785 m²

Velocity V = Q / A

= 0.01 / 0.00785

= 1.27 m/s