CALCULATING PRESSURE LOSS IN TERMS OF FRICTION FOR FLUID
Written by
Ir. Tan Yoke Lee
PECP, MIEM, MiFireE
yokeleetan71@gmail.com
CALCULATING PRESSURE LOSS IN TERMS OF FRICTION FOR FLUID
In general, calculating pressure loss due to friction for fluid flow in pipeline is very important.
ASSUMPTIONS MADE WHEN DOING CALCULATIONS- FLUID IS INCOMPRESSIBLE.
We use Hazen William Equation for water flow.
For non water flow, we need to use a more generalised equation.
That is when Moody’s chart and Darcy Weisbach Equation comes in .
Point to note when using Moody’s chart is that the chart used only for Newtonian fluid where the viscosity is
independent of stress. Reynold’s number (which is a dimensionless number) is expressed in terms of density,
velocity, diameter of pipe and viscosity.
CALCULATING PRESSURE LOSS IN TERMS OF FRICTION FOR FLUID
Darch Weisbach Equation is used to determine the pressure loss in terms of friction. To get the pressure loss, we
need to find the darcy friction factor which can be determined in Moody’s diagram.
Note that Darcy equation has the term density
and thus can be used for fluid that is not water.
However, the fluid must be Newtonian fluid.
CALCULATING PRESSURE LOSS IN TERMS OF FRICTION FOR FLUID
Darch Weisbach Equation is used to determine the pressure loss in terms of friction. Length in equation is
summation of straight pipe length and equivalent pipe length of fittings and valves.
CALCULATING PRESSURE LOSS IN TERMS OF FRICTION FOR FLUID
Moody’s diagram for determining Darcy friction factor. Please note that for non Newtonian fluid, the Reynold’s
number formula in Moody’s diagram is no longer valid. Different approach is required using Fanning friction factor
and different calculation of Reynold’s number.
CALCULATING PRESSURE LOSS IN TERMS OF FRICTION FOR FLUID
1. Calculate
the
Reynold’s number.
2. Calculate
the
relative
pipe
roughness.
3. For the calculated
Reynold’s number,
plot vertical line
until it hits the pipe
relative roughness,
then get the friction
factor.
4. Calculate
the
pressure loss from
Darcy
Weisbach
equation.
CALCULATING PRESSURE LOSS IN TERMS OF FRICTION FOR FLUID
Notes:
• For laminar flow, the
friction factor is not
dependent on the
pipe
roughness
factor.
• For transition flow,
there is no accurate
way of determining
the friction factor,
the value obtained
from
moody’s
diagram is not very
accurate.
• For fully turbulent
flow, the friction
factor is only a
function of the pipe
roughness which is
similar to Hazen
William equation C
value.
CALCULATING PRESSURE LOSS IN TERMS OF FRICTION FOR FLUID
Notes:
When comparing Darcy
to Hazen William for
turbulent flow for water,
Pressure loss in Darcy
when
expressing
velocity in terms of flow
rate and diameter is
proportional to Q^2 and
inversely proportional to
D^5 which is slightly
different from Hazen
William’s equation.
Darcy equation more or
less resonates affinity
law.
CALCULATING PRESSURE LOSS IN TERMS OF FRICTION FOR FLUID
Example for pumping styrene from reservoir:Re= ρVD/µ
ρ= 910kg/m3
Given Flow rate = 2.5m3/hr =0.000694m3/sec
Given D= 0.1m pipe size
Thus V= 0.0884m/sec
µ= 0.000762kg/(m sec)
Re= 82.9 which is laminar flow.
f= 64/Re= 0.772
Given L= 64.8m, Given static gain for pump from
reservoir of styrene= 0.5m (assuming this is the lowest
level of reservoir)
Pressure loss = fL/D (ρV2)/2=0.1096m water
Pressure vapour of styrene= 5mm Hg = 0.0667m water.
NPSH available at pump = 10m (from atmospheric pressure) – 0.0667m – 0.1096m + 0.5m = 10.3m