38 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
The Blasius equation is:R/ u^2 D 0. 0396 Re^0.^25 (equation 3.11)and hence: 15. 21 d^5 D 0. 0396 d/ 1. 77 ð 103 ^0.^25
and: dD 0 .193 m
In order to use the friction chart, Fig. 3.7, it is necessary to assume a value ofR/ u^2 ,
calculatedas above, check the resultant value ofReand calculateR/ u^2 and compare
its value with the assumed value.
IfR/ u^2 isassumedtobeD 0 .0030, then 15. 21 d^5 D 0 .0030 anddD 0 .182 m
∴ ReD 1. 77 ð 103 / 0. 182 D 9750
From Fig. 3.7,R/ u^2 D 0 .0037 which does not agree with the original assumption.
IfR/ u^2 is taken as 0.0024,dis calculatedD 0 .175 m,Reis 1. 0 ð 105 andR/ u^2 D
0 .0022. This is near enough giving the minimum pipe diameterD 0 .175 m.
PROBLEM 3.24
On the assumption that the velocity profile in afluid in turbulentflow is given by the
Prandtl one-seventh power law, calculate the radius at which theflow between it and the
centre is equal to that between it and the wall, for a pipe 100 mm in diameter.
Solution
See Volume 1, Example 3.5.
PROBLEM 3.25
A pipeline 0.5 m diameter and 1200 m long is used for transporting an oil of density
950 kg/m^3 and of viscosity 0.01 Ns/m^2 at 0.4m^3 /s. If the roughness of the pipe surface
is 0.5 mm, what is the pressure drop? With the same pressure drop, what will be the
flowrate of a second oil of density 980 kg/m^3 and of viscosity 0.02 Ns/m^2?
Solution
D 0 .01 Ns/m^2 ,dD 0 .5mandAD/ 4 0. 52 D 0 .196 m^2 ,lD1200 m,
D950 kg/m^3 and:uD 0. 4 / 0. 196 D 2 .04 m/s.
Reynolds numberD ud/ D 950 ð 2. 04 ð 0. 5 / 0. 01 D 9. 7 ð 104
e/dD 0. 5 / 500 D 0 .001 and from Fig. 3.7,R/ u^2 D 0. 0027