PUMPING OF FLUIDS 115
PROBLEM 8.9
A single-acting air compressor supplies 0.1m^3 /s of air (at STP) compressed to 380 kN/m^2
from 101.3kN/m^2 pressure. If the suction temperature is 288.5 K, the stroke is 250 mm,
and the speed is 4 Hz, find the cylinder diameter. Assume the cylinder clearance is 4%
and compression and re-expansion are isentropic
D 1. 4 . What is the theoretical power
required for the compression?
Solution
See Volume 1, Example 8.3.
PROBLEM 8.10
Air at 290 K is compressed from 101.3 to 2000 kN/m^2 pressure in a two-stage compressor
operating with a mechanical efficiency of 85%. The relation between pressure and volume
during the compression stroke and expansion of the clearance gas isPV^1.^25 Dconstant.
The compression ratio in each of the two cylinders is the same and the interstage cooler
may be taken as perfectly efficient. If the clearances in the two cylinders are 4% and 5%
respectively, calculate:
(a) the work of compression per unit mass of gas compressed;
(b) the isothermal efficiency;
(c) the isentropic efficiency
D 1. 4 ;
(d) the ratio of the swept volumes in the two cylinders.Solution
See Volume 1, Example 8.4.
PROBLEM 8.11
Explain briefly the significance of the “specific speed” of a centrifugal or axial-flow pump.
A pump is designed to be driven at 10 Hz and to operate at a maximum efficiency when
delivering 0.4m^3 /s of water against a head of 20 m. Calculate the specific speed. What
type of pump does this value suggest? A pump built for these operating conditions has
a measured overall efficiency of 70%. The same pump is now required to deliver water
at 30 m head. At what speed should the pump be driven if it is to operate at maximum
efficiency? What will be the new rate of delivery and the power required?
Solution
Specific speed is discussed in Section 8.2.3 of Volume 1, where it is shown to be
NsDNQ^1 /^2 /gh^3 /^4. This expression is dimensionless providing that the pump speed,
throughput, and head are expressed in consistent units.