CHEMICAL ENGINEERING

102 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The following table is constructed in the same way.

Distance Outer Inner Area of hm Velocity Volumetric
from duct radius of radius of element (mm) u flowrate
centre line element element m^2 (m/s) Q
(m) (m) (m) m^3 /s

0 0.025 0 0.00196 104 11.1 0.0218

0.05 0.075 0.025 0.0157 100 10.9 0.171

0.10 0.125 0.075 0.0314 96 10.7 0.336

0.15 0.1625 0.125 0.0339 86 10.1 0.342

0.175 0.1875 0.1625 0.0275 79 9.7 0.293

0.20 0.2125 0.1875 0.0314 68 8.9 0.279

0.225 0.2375 0.2125 0.0353 50 7.7 0.272

0.25 0.25 0.2375 0.0192 0 0 0

∑

D 0 .1964 m^2

∑

D 1 .715 m^3 /s

Average velocityD 1. 715 / 0. 1964 D 8 .73 m/s

Mass flowrateD 1. 715 ð 1. 64 D 2 .81 kg/s

uav/umaxD 8. 73 / 11. 1 D 0. 79

ReD 8. 73 ð 1. 64 ð 0. 05 / 1. 9 ð 10 ^5 D 3. 77 ð 104

The velocity distribution in turbulent flow is discussed in Section 3.3.6 where the Prandtl
one-seventh power law is used to give:

uavD 0. 82 umax (equation 3.63)

This is close to that measured in this duct though strictly it only appears at very high
values ofRe. Reference to Fig. 3.14 shows that, atReD 3. 8 ð 104 , the velocity ratio is
about 0.80 which shows remarkably good agreement.