CHEMICAL ENGINEERING

124 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The cross-sectional area of the pipeD/ 4  0. 152 D 0 .0177 m^2.

Velocity of the waterD 0. 05 / 0. 0177 D 2 .82 m/s.

Head loss due to friction is:

hfD 8 R/u^2 l/du^2 / 2 g (equation 3.20)

Thus: 21. 55 D 8 R/u^2  300 / 0. 15  2. 822 / 2 ð 9. 81 

and: R/u^2 D 0. 0033

ReDud/D 1000 ð 2. 82 ð 0. 15 / 10 ^3 D 4. 23 ð 105
From Fig. 3.7,e/dis 0.003.
If, as a result of scaling and fouling, the roughness increases by a factor of 10, the new
value ofe/dD 0 .03. Fig. 3.7 can no longer be used since the new velocity, and hence
the Reynolds number, is unknown. Use is made of equation 3.23 and Fig. 3.8 to find the
new velocity.
The maximum head loss due to friction is still equal to 21.55 m as the pump head is
unchanged.

Thus: 21 .55 mD 21. 55 ð 1000 ð 9. 81 D 211 ,410 N/m^2

R/u^2 Re^2 DPfd^3 / 4 l^2 (equation 3.23)

D 211 , 410 ð 0. 153 ð 1000 / 4 ð 300 ð 10 ^6 D 6. 0 ð 108

From Fig. 3.8,ReD 2. 95 ð 105 whene/dD 0 .03.

Hence the new velocityD 2. 95 ð 105 ð 10 ^3 / 1000 ð 0. 15 D 1 .97 m/s

Reduction in flowD 100  2. 82  1. 97 / 2. 82 D 30 .1percent.