CHEMICAL ENGINEERING

PUMPING OF FLUIDS 113

PROBLEM 8.5

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 0.1m^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.

Solution

See Volume 1, Example 8.6

PROBLEM 8.6

In a single-stage compressor: Suction pressureD 101 .3kN/m^2. Suction temperatureD
283 K. Final pressureD380 kN/m^2. If each new charge is heated 18 deg K by contact
with the clearance gases, calculate the maximum temperature attained in the cylinder.

Solution

The compression ratioD 380 / 101. 3 D 3 .75.
On the first stroke, the air enters at 283 K and is compressed adiabatically to 380 kN/m^2.

Thus: T 2 /T 1 DP 2 /P 1 
^1 /

D 3. 750.^286 D 1. 459

Hence, the exit temperature is:T 2 D 1. 459 ð 283 D413 K

The clearance volume gases which remain in the cylinder are able to raise the temper-
ature of the next cylinder full of air by 18 deg K leaving the cylinder and its contents at
 283 C 18 D301 K. After compression, the exit temperature is:

TD 301 ð 3. 750.^286 D 439 .2K

On each subsequent stroke, the inlet temperature is always 301 K and hence the
maximum temperature attained is 439.2K.

PROBLEM 8.7

A single-acting reciprocating pump has a cylinder diameter of 115 mm and a stroke of
230 mm. The suction line is 6 m long and 50 mm diameter and the level of the water in
the suction tank is 3 m below the cylinder of the pump. What is the maximum speed at
which the pump can run without an air vessel if separation is not to occur in the suction
line? The piston undergoes approximately simple harmonic motion. Atmospheric pressure
is equivalent to a head of 10.4 m of water and separation occurs at pressure corresponding
to a head of 1.22 m of water.