CHEMICAL ENGINEERING

118 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

PROBLEM 8.14

1250 cm^3 /s of water is to be pumped through a steel pipe, 25 mm diameter and 30 m
long, to a tank 12 m higher than its reservoir. Calculate the approximate power required.
What type of pump would you install for the purpose and what power motor (in kW)
would you provide? Viscosity of waterD 1 .30 mN s/m^2. Density of waterD1000 kg/m^3.

Solution

For a 25 mm bore pipe, cross-sectional areaD/ 4  0. 025 ^2 D 0 .00049 m^2.
Viscosity,uD 1250 ð 10 ^6 / 0. 00049 D 2 .54 m/s.

and ReDud/D 1000 ð 2. 54 ð 0. 025 / 1. 3 ð 10 ^3 D 48 , 900

From Table 3.1 the roughnesseof a steel pipe will be taken as 0.045 mm. Hence
e/dD 0. 046 / 25 D 0 .0018.
Whene/dD 0 .0018 andReD 4. 89 ð 104 , from Fig. 3.7R/u^2 D 0. 0032
The pressure drop is then calculated from the energy balance equation and
equation 3.19. For turbulent flow of an incompressible fluid:

u^2 / 2 CgzCvP 2 P 1 C 4 R/u^2 l/du^2 D 0

The pressure drop is:

P 1 P 2 D[u^2 / 2 CgzC 4 R/u^2 l/du^2 ]Df[0. 5 C 4 R/u^2 l/d]u^2 Cgzg

since the velocity in the tank is equal to zero.
Substituting:

P 1 P 2 D 1000 f[0. 5 C 4  0. 0032  30 / 0. 025 ]2. 542 C 9. 81 ð 12 g

D 219 ,500 N/m^2 or 219.5kN/m^2

PowerDG[u^2 / 2 CgzCF]Dkg/sm^2 /s^2 Dm^2 /sN/m^2  (equation 8.60)
D 1. 25 ð 10 ^3  2. 195 ð 105 D275 W
If a pump efficiency of 60% is assumed, the pump motor should be rated at 275 / 0. 6 D
458 W. A single stage centrifugal pump would be suitable for this duty.

PROBLEM 8.15

Calculate the pressure drop in, and the power required to operate, a condenser consisting
of 400 tubes, 4.5 m long and 10 mm internal diameter. The coefficient of contraction at
the entrance of the tubes is 0.6, and 0.04 m^3 /s of water is to be pumped through the
condenser.

Solution

Flow of water through each tubeD 0. 04 / 400 D 0 .0001 m^3 /s.

Cross-sectional area of each tubeD/ 4  0. 01 ^2 D 0 .0000785 m^2.