CHEMICAL ENGINEERING

114 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Solution

The tendency for separation to occur will be greatest at the inlet to the cylinder and at
the beginning of the suction stroke.

If the maximum speed of the pump isNHz, the angular velocity of the driving mech-
anism is 2Nradian/s.

The acceleration of the pistonD 0. 5 ð 0. 23 N^2 cos 2 Nm/s^2.

The maximum acceleration, whentD0, is 4. 54 N^2 m/s^2.

Maximum acceleration of the liquid in the suction pipe is:

 0. 115 / 0. 05 ^2  4. 54 N^2 D 24. 02 N^2 m/s

Accelerating force on the liquidD 24. 02 N^2 / 2  0. 05 ^2 ð 6 ð 1000 .

Pressure drop in suction line due to acceleration

D 24. 02 N^2 ð 6 ð 1000 D 1. 44 ð 105 N^2 N/m^2

D 1. 44 ð 105 N^2 / 1000 ð 9. 81 D 14. 69 N^2 m of water

Pressure head at the cylinder when separation is about to occur:

1. 22 D 10. 4  3. 0  14. 69 N^2 m of water and :ND 0 .65 Hz

PROBLEM 8.8

An air-lift pump is used for raising 0.8 l/s of a liquid of density 1200 kg/m^3 to a height
of 20 m. Air is available at 450 kN/m^2. If the efficiency of the pump is 30%, calculate
the power requirement, assuming isentropic compression of the air
D 1. 4 .

Solution

Volume flow of liquidD800 cm^3 /s or 800ð 10 ^6 m^3 /s

Mass of flowrate of liquidD 800 ð 10 ^6 ð 1200 D 0 .96 kg/s

Work done per secondD 0. 96 ð 20 ð 9. 81 D 188 .4W

Actual work of expansion of airD 188. 4 / 0. 3 D 627 .8W.

The mass of air required per unit time is:

WDPavamlnP/PaDPaValnP/Pa (equation 8.49)

whereVais the volume of air at STP,

Thus: 627. 8 D 101 , 300 Valn 450 / 101. 3 andVaD 0 .0042 m^3

The work done in the isentropic compression of this air is:

P 1 V 1 [

/

 1 ][P 2 /P 1 

^1 /

1] (equation 8.37)

D 101 , 300 ð 0. 0042  1. 4 / 0. 4 [ 450 / 101. 3 ^0.^286 1]D792 J

Power requiredD792 J/sD792 W or 0.79 kW.