CHEMICAL ENGINEERING

PUMPING OF FLUIDS 111

PROBLEM 8.2

A twin-cylinder, single-acting compressor, working at 5 Hz, delivers air at 515 kN/m^2 at
the rate of 0.2m^3 /s. If the diameter of the cylinder is 20 cm, the cylinder clearance ratio
5%, and the temperature of the inlet air 283 K, calculate the length of stroke of the piston
and the delivery temperature.

Solution

For adiabatic conditions,PV^ Dconstant

and: P 2 /P 1 DT 2 /T 1 
/
^1 orT 2 DT 1 P 2 /P 1 
^1 /

Thus the delivery temperatureD 283  515 / 101. 3 ^0.^4 /^1.^4 D500 K

The volume handled per cylinderD 0. 2 / 2 D 0 .1m^3 /s.
Volume per strokeD 0. 1 / 5 D 0 .02 m^3 /s at 515 kN/m^2.
Volume at the inlet conditionD 0. 02 ð 283 / 500 D 0 .0126 m^3 /s.
From equation 8.42, 0. 0126 DVs[1CccP 2 /P 1 ^1 /
]wherecis the clearance and
Vsthe swept volume.

Thus: 0. 0126 DVs[1ð 0. 05  0. 05  515 / 101. 3 ^1 /^1.^4 ]andVsD 0 .0142 m^3

∴ / 4  0. 2 ^2 ðstrokeD 0 .0142 and the strokeD 0 .45 m

PROBLEM 8.3

A single-stage double-acting compressor running at 3 Hz is used to compress air from
110 kN/m^2 and 282 K to 1150 kN/m^2. If the internal diameter of the cylinder is 20 cm,
the length of stroke 25 cm, and the piston clearance 5%, calculate:

(a) the maximum capacity of the machine, referred to air at the initial temperature and

pressure, and

(b) the theoretical power requirements under isentropic conditions.

Solution

The volume per strokeD 2 ð/ 4  0. 2 ^2 ð 0. 25 D 0 .0157 m^3

The compression ratioD 1150 / 110 D 10 .45.

The swept volumeVsis given by:

0. 0157 DVs[1C 0. 05  0. 05  10. 45 ^1 /^1.^4 ]andVsD 0 .0217 m^3 (equation 8.42)

The work of compression/cycle is:

WDP 1 V 1 V 4 

/

 1 [P 2 /P 1 

^1 /

1] (equation 8.41)