Other Friction Losses

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Other Friction Losses

• Valves and Fittings

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Goals

• Calculate frictional losses in a system
  containing valves, fittings, and sudden
  expansions and contractions
• Express frictional losses in terms of velocity
  head
• Assess relative contributions of different
  sources to total viscous dissipation

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Sudden Expansion
Frictional losses occur as result of turbulence
generated immediately downstream of the expansion
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Sudden Expansion
Assume
Ke is the expansion loss coefficient which we
will attempt to describe in terms of flow
properties. How will we do that? Macroscopic
Balances
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Sudden ExpansionMass Balance
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Sudden ExpansionMomentum Balance
Assume turbulent b1 b2 1
0
0
Whats wrong with this?
Replaced Sa with Sb
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Momentum Balance
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Mechanical Energy Balance
Assume turbulent a1 a2 1
0
0
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Combining
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Final Result
Recall Mass Balance Result

• Notes
• Velocity head is based on smaller cross section
• What if flow becomes laminar in large pipe?

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Sudden Contractions
At sudden contractions, flow streamlines converge
causing the downstream developed flow to have an
area smaller than the downstream pipe diameter.
This flow constriction is called the vena
contracta. Viscous dissipation occurs in the
vortices developed in this area.
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Sudden Contraction
Development of an expression for sudden
contraction proceeds in much the same way as that
for sudden expansion with the definition of a
contraction coefficient.
For laminar flow experimentally, Kc lt 0.1 and hfc
is usually neglected
Turbulent (empirical)
Note Calculations again based on small cross
section.
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Valves and Fittings
Note Use the bulk velocity upstream of the
fitting.
Globe valve, wide open Kf 6 Check valve (ball) Kf 70
Angle valve, wide open Kf 2 Check valve (swing) Kf 2
Gate valve Foot valve Kf 15
wide open Kf 0.17 Butterfly valve (5 closed) Kf 0.24
half open Kf 4.5 Standard water meter Kf 7
Elbow Return bend Kf 1.5
90 Kf 0.75 Tee Kf 1
45 Kf 0.35
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Summary for Fittings
For a group of fittings and expansions/contraction
s note that the form of the equation for hf is
the same, a coefficient multiplied by the
velocity head. As long a the bulk average
velocity is the same (same diameter piping) for a
given pipe segment, the following expression can
be used for the overall friction loss term.
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Alternate Method
The previous equation can be manipulated to
change the Kf values into equivalent lengths of
pipe (see attached table) of diameter D. When
this method is used the equivalent lengths are
add to the length of the actual pipe sections and
the equation becomes.
Note The values in the table are L/D and must
be multiplied by D to get equivalent lengths.
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Velocity Heads
The above expression shows that friction loss in
a complicated flow system can be expressed as a
number of velocity heads. It is a measure of
momentum loss resulting from flow through the
system. For instance in making a 90 turn all
x-momentum is turned into y-momentum.
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Valve Video Notes
Gate On/Off
Globe Flow Control (small system)
Plug On/Off
Ball On/Off
Butterfly Flow Control (large system)
Diaphragm Toxic or Corrosive Fluids
Check Flow Direction
Control Flow Control
Solenoid On/Off
Valve Types and Uses
Hydraulic Shocks Bypass lines for High ?p Valves
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Example
Water is pumped at 250 gpm from tank 1 to tank 2
as shown. Calculate the required power input to
the pump assuming a pump efficiency of 70.
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Practical Use of Velocity HeadsIn Making Design
Calculations
To calculate the importance of various terms in
hf, compare 4f(L/D) to Ki. If 4f(L/D) gtgt Ki,
then effect of fittings can be neglected.
Suppose 4f(L/D) 1. Then hf is equivalent to 1
velocity head. Is there a quick way to determine
the number of velocity heads loss for a given
length of pipe?
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Friction Loss Estimates
4f(L/D) 1 is equivalent to
For turbulent flow, f typically varies from 0.002
0.01, which corresponds to L/D values of 125
25. For ordinary practice an average f of 0.005
is not unusual and leads to L/D 50.
This means that 50 pipe diameters will generate a
friction loss equal to about one velocity head.
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Estimate of Friction Losses
To estimate friction loss in a actual pipe system
use the following equation
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Example
A 3-in diameter pipe, 180 ft in length, contains
one gate valve (wide open) and a 90 elbow.
Determine the largest source of viscous
dissipation by comparing velocity heads.
Fittings
Pipe
Since 14.4 gtgt 0.92 friction losses in the pipe
outweigh the losses in the fittings and the
fittings can be ignored. What if L 12 ft?