CHEMICAL ENGINEERING

FLOW IN PIPES AND CHANNELS 35

PROBLEM 3.20

Oil of viscosity 10 mNs/m^2 and specific gravity 0.90,flows through 60 m of 100 mm
diameter pipe and the pressure drop is 13.8 kN/m^2. What will be the pressure drop for
a second oil of viscosity 30 mNs/m^2 and specific gravity 0.95flowing at the same rate
through the pipe? Assume the pipe wall to be smooth.

Solution

For thefirst oil, with a velocity in the pipe ofum/s then:

ReDuð 0. 90 ð 1000 ð 100 / 1000 / 10 ð 10 ^3 D 9000 u

R

u^2

Re^2 D

Pd^3

4 l^2

D 13. 8 ð 1000 ð 0. 103 ð 900 / 4 ð 60 ð 0. 012 D 5. 2 ð 105

From Fig. 3.8, whenR/u^2 Re^2 D 5. 2 ð 105 for a smooth pipe,ReD12000.

Hence, velocityuD 12 , 000 / 9000 D 1 .33 m/s.

For the second oil, the same velocity is used although the density and viscosity are now
950 kg/m^3 and 0.03 Ns/m^2.

Hence: ReD 1. 33 ð 0. 10 ð 950 / 0. 03 D 4220

For a smooth pipe, Fig. 3.7 gives a friction factor,R/u^2 D 0 .0048 for this value of
Re.
From Equation 3.18:

PD 4 R/u^2 l/du^2

D 4 ð 0. 0048 ð 60 / 0. 10 ð 950 ð 1. 332

D 1. 94 ð 104 N/m^2 19 .4kN/m^2

PROBLEM 3.21

Crude oil is pumped from a terminal to a refinery through a 0.3 m diameter pipeline.
As a result of frictional heating, the temperature of the oil is 20 deg K higher at the
refinery end than at the terminal end of the pipe and the viscosity has fallen to one half
its original value. What is the ratio of the pressure gradient in the pipeline at the refinery
end to that at the terminal end? Viscosity of oil at terminalD90 mNs/m^2. Density of oil
(approximately constant)D960 kg/m^3. Flowrate of oilD 20 ,000 tonne/day.
Outline a method for calculating the temperature of the oil as a function of distance
from the inlet for a given value of the heat transfer coefficient between the pipeline and
the surroundings.