120 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
PowerDmass flowrateðheadðg (equation 8.61)D 3. 0 ð 37. 6 ð 9. 81 D1105 WIf the pump is 50% efficient, power requiredD 1105 / 0. 5 D2210 W or 2.2kW.
For this duty a PTFE lined pump and lead piping would be suitable.PROBLEM 8.17
60% sulphuric acid is to be pumped at the rate of 4000 cm^3 /s through a lead pipe
25 mm diameter and raised to a height of 25 m. The pipe is 30 m long and includes two
right-angled bends. Calculate the theoretical power required. The density of the acid is
1531 kg/m^3 and its kinematic viscosity is 4. 25 ð 10 ^5 m^2 /s. The density of water may
be taken as 1000 kg/m^3.
Solution
Cross-sectional area of pipeD/ 4 0. 025 ^2 D 0 .00049 m^2
Velocity,uD 4000 ð 10 ^6 / 0. 00049 D 8 .15 m/s.
ReDud/ Dud/ /D 8. 15 ð 0. 025 / 4. 25 ð 10 ^5 D 4794
If e is taken as 0.05 mm from Table 3.1, e/dD 0 .002 and from Fig. 3.7,
R/u^2 D 0 .0047.
Head loss due to friction is given by:
hfD 4 R/u^2 l/du^2 /g (equation 3.20)D 4 ð 0. 0047 30 / 0. 025 8. 152 / 9. 81 D 152 .8mandzD 25 .0mFrom Table 3.2, 0.8 velocity headsu^2 / 2 gare lost through each 90°bend so that the
loss through two bends is 1.6 velocity heads or 1. 6 ð 8. 152 / 2 ð 9. 81 D 5 .4m.
Total head lossD 152. 8 C 25 C 5. 4 D 183 .2m.
Mass flowrateD 4000 ð 10 ^6 ð 1. 531 ð 1000 D 6 .12 kg/s.
From equation 8.61 the theoretical power requirementD 6. 12 ð 183. 2 ð 9. 81 D
11 ,000 W or 11.0kW.
PROBLEM 8.18
1.3 kg/s of 98% sulphuric acid is to be pumped through a 25 mm diameter pipe, 30 m
long, to a tank 12 m higher than its reservoir. Calculate the power required and indicate
the type of pump and material of construction of the line that you would choose. Viscosity
of acidD 0 .025 N s/m^2. DensityD1840 kg/m^3.