NOR DIANA BINTI ABDUL RAHMAN
NUR AMALINA BINTI MUHAMAD HANAFI.
NUR FARAH WAHIDA BINTI ABU HASSAN.
AMAL HAYATI BINTI CHE MAT RAPI
PUAN NOOR ASSIKIN BINTI ABD WAHAB.
As the water flows from a faucet at a very low
velocity, the flow appears to be smooth and steady.
The stream has a fairly uniform diameter and there
is little or no evidence of mixing of the various parts
of the stream.
This is called laminar flow, a term derived from the
word layer, because the fluid appears to be flowing
in continuous layers with little or no mixing from one
layer to the adjacent layers.
When the faucet is nearly fully
open, the water has a rather high
The elements of fluid appear to be
mixing chaotically within the
stream. This is a general
description of turbulent flow.
The behavior of a fluid, particularly with regard to
energy losses, it quite dependent on whether the
flow is laminar or turbulent, as will be demonstrated
later in this chapter.
For this reason we need a means of predicting the
type of flow without actually observing it.
Indeed, direct observation is impossible for fluids in
It can be shown experimentally and
verified analytically that the character of
flow in depends on four variables:
fluid density, fluids viscosity , Pipe
diameter D, and average velocity of flow .
Osborne Reynolds was the first to
demonstrate that laminar or turbulent flow
can be predicted if the magnitude of a
dimensionless number, now called the
Reynolds number (NR), is known.
Table 8.1 lists the required units in
both the SI metric unit system and the
U.S. customary unit system.
Converting to these standard units
prior to entering data into the
calculation for NR is recommended
We can demonstrate that the Reynolds
number is dimensionless by
substituting standard SI units into Eq.
We can demonstrate that the Reynolds number is
dimensionless by substituting standard SI units into
Because all units can be cancelled, NR is
TABLE 8.1 Standard units for quantities used in the
calculation of Reynolds number to ensure that it is
Quantity SI Units U.S. Customary Units
Diameter m ft
Density Kg/m3 or
N.s/m2 or Pa.s
CRITICAL REYNOLDS NUMBERS
for practical applications in pipe flow we find
that if the Reynolds number for the flow is
less than 2000, the flow will be laminar.
If the Reynolds number is greater than
4000, the flow can be assumed to be
In the range of Reynolds number between
2000 and 4000, it is impossible to predict
which type of flow exist; therefore this range
is called the critical region.
Typical applications involve flow that
are well within the laminar flow range
or well within the turbulent flow range,
so the existence of this region of
uncertainty does not cause great
If the flow in a system is found to be in
the critical region, the usual practice is
to change the flow rate or pipe
diameter to cause the flow to be
definitely laminar or turbulent.
More precise analysis is then possible.
By carefully minimizing external
disturbances, it is possible to maintain
laminar flow for Reynolds numbers as high
However, when NR is greater than about
4000, a minor disturbance of the flow
stream will cause the flow to suddenly
change from laminar to turbulent.
For this reason, and because we are
dealing with practical applications in this
book, we assume the following:
If NR < 2000, the flow is laminar.
If NR >4000, the flow is turbulent.
in the general energy equation
the term hL is defined as the energy loss from the
system. one component of the energy loss is due to
friction in the flowing fluid.
one component of the energy loss is due to friction in the
flowing fluid. friction is proportional to the velocity head of
the flow and to the ratio of the length to the diameter of
the flow stream, for the case of flow in pipes and tubes.
this is expressed mathematically as Darcy’s equation:
hL = energy loss due to friction (Nm/N,m,lb-ft/lb, or ft)
L = length of flow stream of flow stream (m or ft)
D = pipe diameter (m or ft)
f = friction factor (dimensionless)
FRICTION LOSS IN LAMINAR FLOW
when laminar flow exists, the fluid seems to flow as
several layers, one on another.
because of the viscosity of the fluid, a shear stress
is created between the layers of fluid.
energy is lost from the fluid by the action of
overcoming the frictional forces produced by the
because laminar flow is so regular and orderly, we
can derive a relationship between the energy loss
and the measurable parameters of the flow system.
this relationship is known as the hagen poiseuille
the Hagen-Poiseuile equation is valid only for
laminar flow (NR <2000).
however we stated earlier that Darcy’s equation,
equation (8-3), could also be used to calculate the
friction loss for laminar flow.
if the two relationships for hL are set equal to each
other, we can solve for the value of the friction
Because ρ = γ/g, we get
The Reynolds number is defined as NR = υDρ/µ.
Then we have
In summary, the energy loss due to friction in laminar
flow can be calculated either from the hagen-
Or from Darcy’s equation,
Where ƒ= 64/NR.
FRICTION LOSS IN TURBULENT FLOW
For turbulent flow of fluids in circular pipes it is most
convenient to use Darcy’s equation to calculate the
energy loss due to friction.
Turbulent flow is rather chaotic and is constantly
For these reasons we must rely on experimental data to
determine the value of ƒ.
Test have shown that dimensionless number ƒ is
dependent on two other dimensionless numbers, the
Reynolds number and relative roughness of the pipe.
The relative roughness is the ratio of the pipe diameter
D to the average pipe wall roughness є (Greek letter
Figure 8.5 illustrates pipe wall roughness
(exaggerated) as the height of the peaks of the
The condition of the pipe surface is very much
dependent on the pipe material and the method of
Because the roughness is somewhat irregular,
averaging techniques are used to measure the overall
THE MOODY DIAGRAM
One of the most widely used methods for
evaluating the friction factor employs the Moody
diagram shown in Fig.8.6.
The diagram shows the friction factor f plotted
versus the Reynolds number NR, with a series of
parametric curves related to the relative roughness
explanation of parts of moody’s diagram..docx
USE OF THE MOODY DIAGRAM
The Moody Diagram is used to help determine the
value of the friction factor f for turbulent flow.
The value of the Reynolds number and the relative
roughness must be known.
Therefore, the basic data required are the pipe
inside diameter, the pipe material, the flow velocity,
and the kind of fluid and its temperature, from which
the viscosity can be found.
The following example problems illustrate the
procedure for finding f.
EQUATION FOR THE FRICTION
The moody diagram in Fig. 8.6 is a convenient and
sufficiently accurate means of determining the
value of the friction factor when solving problems by
However, if the calculation are to be automated for
solution on a computer or a programmable
calculator, we need equation for the friction factor.
In the laminar flow zone. For values below 2000,
can be found from Eq. (8-5).
= 64 / R
The following equations, which allows the direct
calculation of the value of the friction factor for
turbulent flows, was developed by P.K. Swamee and
A.K. Jain and is reported in Reference 3 :
HAZEN WILLIAMS FORMULA FOR
The Darcy equation presented in this chapter for
calculating energy loss due to friction is applicable
for any Newtonian fluid.
An alternate approach is convenient for the special
case of the flow of water in pipeline systems.
The Hazen Williams formula is unit-specific. In the
U.S. Customary unit system it takes the form.
V= Average velocity of flow (ft/s)
Cℎ = Hazen Williams coefficient (dimensionless)
R= Hydraulic radius of flow conduit (ft)
S= Ratio of ℎL/: energy loss/length of conduit (ft/ft)
The Hazen Williams formula for SI unit is
NOMOGRAPH FOR SOLVING THE
The nomograph shown in Fig.8.9. allows the solution
of the Hazen-Williams formula to be done by simply
aligning known quantities with a straight edge and
reading the desired unknowns at the intersection of
the straight edge with the appropriate vertical axis.
Note that this nomograph is constructed for the value
of the Hazen Williams coefficient of If the actual pipe
condition warrants the use of a different value of the
following formulas can be used to adjust the results.
The subscript ”100” refers to the value read from
the nomograph for .
The subscript “” refers to the value for the given.
FINAL EXAM:20 DAYS
Saturday, July 27, 2013