Pressure Drop due to Friction 41
Consider a 16 in. pipeline, with a wall thickness of 0.250 in.,
transporting a liquid of viscosity 250 cSt. At a flow rate of 50,000 bbl/day
the Reynolds number is, using Equation (3.16),
R=92.24(50,000)/(250×15.5)=1190
Since R is less than 2000, this flow is laminar. If the flow rate is tripled to
150,000 bbl/day, the Reynolds number becomes 3570 and the flow will be
in the critical region. At flow rates above 168,040 bbl/day the Reynolds
number exceeds 4000 and the flow will be in the turbulent region. Thus,
for this 16 in. pipeline and given liquid viscosity of 250 cSt, flow will be
fully turbulent at flow rates above 168,040 bbl/day.
As the flow rate and velocity increase, the flow regime changes. With
changes in flow regime, the energy lost due to pipe friction increases. At
laminar flow, there is less frictional energy lost compared with turbulent flow.
3.4 Flow Regimes
In summary, the three flow regimes may be distinguished as follows:
Laminar: Reynolds number<2000
Critical: Reynolds number>2000 and Reynolds number<4000
Turbulent: Reynolds number>4000
As liquid flows through a pipeline, energy is lost due to friction between
the pipe surface and the liquid and due to the interaction between liquid
molecules. This energy lost is at the expense of liquid pressure. (See
Equation (2.37), Bernoulli’s equation, in Chapter 2.) Hence we refer to the
frictional energy lost as the pressure drop due to friction.
The pressure drop due to friction in a pipeline depends on the flow rate,
pipe diameter, pipe roughness, liquid specific gravity, and viscosity. In
addition, the frictional pressure drop depends on the Reynolds number
(and hence the flow regime). Our objective would be to calculate the
pressure drop given these pipe and liquid properties and the flow regime.
The pressure drop due to friction in a given length of pipe, expressed in
feet of liquid head (h), can be calculated using the Darcy-Weisbach
equation as follows:
h=f(L/D)(V
2
/2g) (3.19)
where
f=Darcy friction factor, dimensionless, usually a number between 0.008
and 0.10
L=Pipe length, ft
D=Pipe internal diameter, ft
Copyright © 2004 by Marcel Dekker, Inc.