CHEMICAL ENGINEERING

FLOW IN PIPES AND CHANNELS 37

106 N/m^2. What will the pressure drop be at the sameflowrate if it is necessary to replace
the pipe by one only 300 mm in diameter? Assume the pipe surface to be smooth.

Solution

D 0 .01 Ns/m^2 , D900 kg/m^3 ,dD 0 .50 m,lD10000 m andPD 1 ð 106 N/m^2.

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

D 1. 106 ð 0. 503 ð 900 / 4 ð 10000 ð 0. 012 D 2. 81 ð 107

From Fig. 3.8,ReDud/ D 1. 2 ð 105
uDRe /d
D 1. 2 ð 105 ð 0. 01 / 900 ð 0. 50 D 2 .67 m/s

If the diameter of the new pipe is 300 mm, the velocity is then:

D 2. 67 ð 0. 5 / 0. 3 ^2 D 7 .42 m/s

Reynolds numberD 7. 42 ð 0. 30 ð 900 / 0. 01 D 2. 0 ð 105

From Fig. 3.7,R/u^2 D 0 .0018 and from equation 3.18:

PD 4 ð 0. 0018 ð 10000 / 0. 3 ð 900 ð 7. 422 D 1. 19 ð 107 N/m^2

PROBLEM 3.23

Oil of density 950 kg/m^3 and viscosity 10^2 Ns/m^2 is to be pumped 10 km through a
pipeline and the pressure drop must not exceed 2ð 105 N/m^2. What is the minimum
diameter of pipe which will be suitable, if aflowrate of 50 tonne/h is to be maintained?
Assume the pipe wall to be smooth. Use either a pipe friction chartorthe Blasius equation
R/u^2 D 0. 0396 Re^1 /^4 .

Solution

From equation 3.6 a force balance on thefluid in the pipe gives:

RDPd/ 4 l

or: D 2 ð 105 d/ 4 ð 104 D 5 d

Velocity in the pipeDG/A
D 50 ð 1000 / 3600 / 950 ð/ 4 d^2 D 0. 186 /d^2

Hence: R/u^2 D 5 d/ 950 ð 0. 186 /d^2 ^2 D 15. 21 d^5

ReDud/

D 0. 186 ðd^2 ðdð 950 / 1 ð 10 ^2 D 1. 77 ð 103 /d