Pipe Flows Filled

Florida International University
CWR 3201 - Fluid Mechanics, Fall 2018
Fluid Flow in Pipes (Single-pipe)
Arturo S. Leon, Ph.D., P.E., D.WRE

Learning Objectives
(1) Identify and understand various characteristics of flows

in pipes
(2) Discuss the main properties of laminar and turbulent
flows
(3) Calculate losses, flow rates and pipe diameters in a
single piping system
Video of pipe flows
3D Petrochemical Refinery
https://www.youtube.com/watch?v=tkmozP-97M4
Typical components of
a pipe system
General Characteristics of pipe flow
Pipe flow Open-channel flow

Laminar or Turbulent Flow?
(http://www.youtube.com/watch?v=WG-YCpAGgQQ)
Laminar or Turbulent Flow?
Typical dye streaks

Fully Developed Flow
Example: P7.21. A laboratory experiment is designed to create a
laminar flow in a 2-mm diameter tube shown in Fig.P7.21. Water
flows from a reservoir through the tube. If 18 liters is collected in
2 hours can the entrance length be neglected?
Turbulent Flow in a Pipe
7.6.2 Velocity Profile
e or  = Average wall roughness height

δv = Viscous wall layer thickness
• Hydraulically smooth: The viscous wall thickness (δv) is large enough that
it submerges the wall roughness elements Negligible effect on the flow
(almost as if the wall is smooth).
• If the viscous wall layer is very thin Roughness elements protrude off the
layer The wall is rough.
• The relative roughness e/D (or /D) and Reynolds number can be used to
find if a pipe is smooth/rough.
Energy considerations
Major losses
Major Losses in Developed Pipe Flow
• Most calculated quantity in pipe flow is the head loss.
• Allows pressure change to be found pump selection.
Head loss from wall shear in a developed flow is related to the friction
factor(f).
• f = f(ρ, μ, V, D, )
• Darcy-Weisbach equation
The Moody diagram
Major Losses in Developed Pipe Flow
• Moody diagram is a plot of experimental data relating friction

factor to the Reynolds number.
• For a given wall roughness There is a large enough Re to get
a constant friction factor Completely turbulent regime.
• For smaller relative roughness As Re decreases, friction
factor increases Transition zone Friction factor becomes
like that of a smooth pipe.
• For Re < 2000 The critical zone couples the turbulent flow to
the laminar flow and may represent an oscillatory flow that
alternately exists between turbulent and laminar flow.
• Assume new pipes As a pipe gets older, corrosion occurs
changing both the roughness and the pipe diameter.
Friction factor for the entire nonlaminar range
(smooth + completely turbulent regime)
Empirical equations for Re > 4000
Colebrook formula
Haaland formula (To avoid trial-and-error

Major Losses in Noncircular Conduits
• Can approximate for conduits with noncircular cross sections:
• Using hydraulic radius R
A: Cross-sectional area
P: Wetted perimeter Perimeter where
the fluid is in contact with the solid
boundary
• E.g., for a circular pipe:

• Hydraulic radius R =
• The head-loss then becomes:

Example: P.7.112. Water at 20oC is transported through a
2 cm x 4 cm smooth conduit and experiences a pressure drop
of 80 Pa over a 2-m horizontal length. What is the flow rate?
Minor losses
Swing check valve video
http://www.youtube.com/watch?v=Krp6pOnaNsk
Minor losses (Cont.)
• Sometimes minor losses (from fittings that
cause additional losses) can exceed
frictional losses.
• Expressed in terms of a loss coefficient K.
• K can be determined experimentally.

Minor Losses in Pipe Flow
• A loss coefficient can be expressed as an equivalent length Le

of pipe:
• For long segments of pipe, minor losses can usually be

neglected.
Entrance flow conditions and
loss coefficient
Reentrant Sharp edged

(KL = 0.8) (KL = 0.5)
Slightly rounded Well rounded

(KL = 0.2) (KL = 0.04)
Exit flow conditions and loss
coefficient
Reentrant Sharp edged
Slightly rounded Well rounded

Loss coefficients for Pipe Components
Threaded elbow
Flanged elbow
Example:
Water flows from the container shown in Fig. 8.59. Determine
the loss coefficient needed in the valve if the water is to
“bubble up” 3 in above the outlet pipe. The entrance is slightly
rounded.
Figure 8.59
Example: P.7.129. What is the maximum flow rate through the
pipe shown in Figure P.7.129 if the elevation difference of the
reservoir surfaces is 80 m.
Example:
A 40-m long, 12-mm diameter pipe with a friction factor of 0.020
is used to siphon 30C water from a tank as shown in Fig. 8.50.
Determine the maximum value of h allowed if there is to be no
cavitation within the hose. Neglect minor losses.
Figure 8.50
Florida International University
CWR 3201 - Fluid Mechanics, Fall 2018
Pipe Networks
Arturo S. Leon, Ph.D., P.E., D.WRE

Pipe networks
(b)
Frictional Losses in Pipe Elements
Frictional losses in piping are commonly evaluated using the
Darcy–Weisbach or Hazen–Williams equation. The Darcy–
Weisbach formulation provides a more accurate estimation.
Where:
hL = head loss over length L of pipe
R = Resistance coefficient (This is not hydraulic radius)
Q = discharge in the pipe
 = exponent
Darcy-Weisbach relation ( = 2)
Swamee-Jain
Haaland
Hazen–Williams equation (For Water)
Where:
C = Hazen–Williams roughness coefficient, m = 4.87,  = 1.85
11.2 Losses in Piping Systems
Simple Pipe Systems
Series Piping System
Parallel Piping System

Branch Piping
Approximation of
pump curves:
Hp = actual head gained by

the fluid from the pump
Method for Analyzing pipe Networks
Method used in Flows in Pipe Networks
Example (Proposed problems):
The three water filled-tanks shown in Fig P.8.114 are connected by pipes as
indicated. If minor losses are neglected, determine the flow rate in each pipe.
Use Flows in Pipe Networks (http://web.eng.fiu.edu/arleon/Pipe_Network.html)
or EPANET (https://www.epa.gov/water-research/epanet)
Show demo Figure 8.114
B
A
C30 C29
C28 C
D
Example
. 11.7. For the piping system (commercial steel) shown below,
determine the flow distribution and piezometric heads at the junctions.
Use the EPANET Model (https://www.epa.gov/water-research/epanet).
Show demo on
how to use the
EPANET Model
Important Considerations in EPANET
EPANET defaults to gallons per minute and other Customary US
units. To change to SI units do the following:
Project > Analysis Options... > Flow Units > LPS (or LPM or
other SI units for flow ) (This also changes units for pipe lengths
and head to meters and pipe diameters to mm.)
• Length: The actual length of the pipe in feet (meters)

• Diameter: The pipe diameter in inches (mm)
• Roughness: The roughness coefficient of the pipe. It is unitless
for Hazen-Williams or Chezy-Manning roughness and has units of
millifeet (mm) for Darcy-Weisbach roughness.
• Loss Coefficient: Unitless minor loss coefficient associated with
bends, fittings, etc. Assumed 0 if left blank.
• Initial Status: Determines whether the pipe is initially open,
closed, or contains a check valve. If a check valve is specified
then the flow direction in the pipe will always be from the
Start node to the End node
Results:
Results (Cont.):

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Florida International University

CWR 3201 - Fluid Mechanics, Fall 2018

Fluid Flow in Pipes (Single-pipe)

Arturo S. Leon, Ph.D., P.E., D.WRE

(1) Identify and understand various characteristics of flows

Pipe flow Open-channel flow

Typical dye streaks

e or  = Average wall roughness height

• Moody diagram is a plot of experimental data relating friction

Haaland formula (To avoid trial-and-error

• E.g., for a circular pipe:

• The head-loss then becomes:

• K can be determined experimentally.

• A loss coefficient can be expressed as an equivalent length Le

• For long segments of pipe, minor losses can usually be

Reentrant Sharp edged

Slightly rounded Well rounded

Reentrant Sharp edged

Slightly rounded Well rounded

Arturo S. Leon, Ph.D., P.E., D.WRE

Parallel Piping System

Hp = actual head gained by

Show demo Figure 8.114

• Length: The actual length of the pipe in feet (meters)

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