3. History
• In 1939, Cyril F. Colebrook combined the available data for transition
and turbulent flow in smooth as well as rough pipes into the Colebrook
equation:
• In 1942, the American engineer Hunter Rouse verified Colebrook’s
equation and produced a graphical plot of f.
4. • In 1944, Lewis F. Moody redrew Rouse’s diagram into the form
commonly used today, called Moody chart
• Performers 10,000 experiment.
• It is no way to find a mathematical closed form for friction factor by
theoretical analysis; therefore, all the available results are obtained from
painstaking experiments.
• Plotted the Chart b/w Darcy – Weisbach friction factor fD against
Reynolds number Re for various values of relative roughness ε / D.
History
5. LAMINAR AND TURBULENT FLOWS
• Laminar flow: characterized by smooth streamlines and
highly ordered motion.
• Turbulent flow: characterized by velocity fluctuations and
highly disordered motion.
• The transition from laminar to turbulent flow does not
occur suddenly; rather, it occurs over some region in which
the flow fluctuates between laminar and turbulent flows
before it becomes fully turbulent.
6. Reynolds Number
• British engineer Osborne Reynolds (1842–1912) discovered that the flow regime depends
mainly on the ratio of inertial forces to viscous forces in the fluid.
• The ratio is called the Reynolds number and is expressed for internal flow in a circular pipe as
7. Reynolds Number
• For flow through noncircular pipes, the Reynolds
number is based on the hydraulic diameter Dh
defined as
• Ac = cross-section area
• P = wetted perimeter
• The transition from laminar to turbulent flow
also depends on the degree of disturbance of the
flow by surface roughness, pipe vibrations, and
fluctuations in the flow.
9. Pressure Drop
• The pressure drop represents the pressure loss ∆PL
• In practice, it is found convenient to express the pressure loss for all types of fully
developed internal flows as
It is also called the Darcy–Weisbach friction factor, named after the Frenchman Henry
Darcy (1803–1858) and the German Julius Weisbach (1806–1871)
11. • For laminar flow, the friction factor
decreases with increasing Reynolds
number, and it is independent of surface
roughness
• The friction factor is a minimum
for a smooth pipe and increases
with roughness
• The data in the transition region
are the least reliable.
12. Observations from the Moody chart
• In the transition region, at small relative roughness's, the friction factor increases and
approaches the value for smooth pipes.
• At very large Reynolds numbers, the friction factor curves corresponding to
specified relative roughness curves are nearly horizontal, and thus the friction factors
are independent of the Reynolds number. The flow in that region is called fully rough
turbulent flow or just fully rough flow
13. Variables:
roughness • Roughness is important in the viscous sub-layer in
turbulent flows, if it protrudes sufficiently in this layer.
• Then range of roughness for validity of this
analysis is for:
Then, the dimensionless groups are the following:
• The viscous layer in laminar flow is so large, that small
roughness does not play a role.
14. Dimensional Analysis of Pipe Flow
For fully developed pipe flow in a horizontal pipe:
a’s account for non-uniform velocity profiles
Darcy-Weisbach Equation
15. The Moody Chart
• Basically for turbulent flow
• When solving many fluid dynamics problems, be it steady state or transient, the Darcy-
Weisbach friction factor, f, is necessary. In circular pipes this factor can be solved directly
with the Swamee-Jain equation, as well as others, however most of these equations are
complicated, and become cumbersome when iteration is necessary. Therefore, it is often
effective to solve for this friction factor using the Moody Chart.
16. Procedure to read the Moody’s Chart
• Calculate the Reynolds Number
• Compute relative roughness
• The wall roughness may be zero, making the relative roughness zero, this does NOT
mean that the friction factor will be zero.
• Find the line referring to your relative roughness on the right side of the diagram
• Follow this line to the left as it curves up until to reach the vertical line
corresponding to your flow's Reynolds Number.
17. • Mark this point on the Chart.
• Using a straight edge, follow the point straight left, parallel to the
x axis, until you reach the far left side of the chart
• Read off the corresponding friction factor
• Calculate the energy losses knowing the friction factor.
• Calculate a new velocity and Reynolds Number.
Procedure to read the Moody’s Chart
19. Pumps
• A device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action
• Three groups:
• Direct lift
• Displacement
• Gravity pumps
20. Pumps
• Pump’s performance is described by the following parameters:
• Capacity
• Head
• Power
• Efficiency
• Net positive suction head
• Specific speed
• Capacity, Q, is the volume of water delivered per unit time by the pump (usually gpm)
21. Piping Networks
• Two general types of networks
• Pipes in series
• Volume flow rate is constant
• Head loss is the summation of parts
• Pipes in parallel
• Volume flow rate is the sum of the
components
• Pressure loss across all branches is the same
22. Piping Networks and Pump Selection
• For parallel pipes, perform CV analysis between points A
and B
• Piping Networks and Pump Selection
23. Pump Performance: power
• The power imparted into a fluid increases the energy of the fluid per
unit volume
• Power to operate a pump is directly proportional to discharge head,
specific gravity of the fluid (water), and is inversely proportional to
pump efficiency
• Usually determined by brake horsepower (BHP)
• BHP = power that must be applied to the shaft of the pump by a
motor to turn the impeller and impart power to the water
24. Pumping Power
• Head is the net work done on a unit of water by the pump and is given by the following equation
• Hs = SL + DL + DD + hm + hf + ho + hv
• Hs = system head, SL = suction-side lift, DD = water source drawdown, hm = minor losses (as
previous), hf = friction losses (as previous), ho = operating head pressure, and hv = velocity head
(V2/2g)
• Suction and discharge static lifts are measured when the system is not operating
• DD, drawdown, is decline of the water surface elevation of the source water due to pumping (mainly for
wells)
• DD, hm, hf, ho and hv all increase with increased pumping capacity, Q
25. Pump Performance: efficiency
• Ep = 100(WHP/BHP) = output/input
• Ep never equals 100% due to energy losses such as
friction in bearings around shaft, moving water against
pump housing, etc
• Centrifugal pump efficiencies range from 25-85%
• If pump is incorrectly sized, Ep is lower
26. Pump Performance: suction head
• Conditions on the suction side of a pump can impart limitations on pumping
systems
• What is the elevation of the pump relative to the water source?
• Static suction lift (SL) = vertical distance from water surface to centerline of the
pump
• SL is positive if pump is above water surface, negative if below
• Total suction head (Hs) = SL + friction losses + velocity head:
Hs = SL + (hm + hf) + V2
s/2g
27. Pump Performance Curves
• Report data on a pump relevant to head, efficiency,
power requirements, and net positive suction head to
capacity
• Each pump is unique dependent upon its geometry
and dimensions of the impeller and casing
• Reported as an average or as the poorest performance
28. Characteristic Pump Curves
• Head as capacity
• Efficiency as capacity , up to a point
• BHP as capacity , also up to a point
• REM:
• BHP = 100QHS/Ep3,960
