Experiment 5
Pipe Flow-Major and Minor losses ( review)
•
The goal is to study pressure losses due to viscous ( frictional) effects in fluid
flows through pipes
Differential Pressure
Gauge- measure ΔP
H
Flow meter
D
Reservoir
Pipe
L
Valve
Schematic of experimental Apparatus
•
Pipes with different Diameter, Length, and surface characteristics will be used
for the experiments
Major and Minor losses
Total Head Loss( hLT)
= Major Loss (hL)+ Minor Loss (hLM)
Due to wall friction
LV2
Darcy' s Equation hl  f
D 2g
In this experiment you will find
friction factor for various pipes
Due to sudden expansion,
contraction, fittings etc
hlm
V2
K
2g
K is loss coefficient must be
determined for each situation
For Short pipes with multiple fittings, the minor losses are no longer
“minor”!!
Major loss
Differential Pressure Gaugemeasure ΔP
L
ρ
V
ε
Pipe
D
•
μ
Physical problem is to relate pressure drop to fluid parameters and pipe
geometry
P(  ,V , L,  , D,  )
Using dimensional
analysis we can show
that
 VD L  
 
, , 
 D D
1
2


V


2


P
Friction factor
P
1
2
 V 
2


L  VD  

, 
D   D
L  VD   1

 P   
,  V 2 
D   D  2

 VD  
define friction factor f   
, 
  D
LV2
hL  f
L 1
2
ie P  f  V 
D 2g
D 2

D
1
L1
2
 f  PL
or PL  f
V
D2
L 1
2

V


2
PL
LV
2

 hL  f
g
D 2g
Friction Factor
 VD  
f  
, 
  D
•


f  Re, 
D

For Laminar flow ( Re<2300) inside a horizontal pipe, friction factor is
independent of the surface roughness.
ie f Re  only.
Theoretically we can derive the functional relationship as
64
f 
Re
•
•
For Laminar flow
For Turbulent flow ( Re>4000) it is not possible to derive analytical
expressions.
Empirical expressions relating friction factor, Reynolds number and
relative roughness are available in literature
Friction factor correlations
  / D   2.51
1
Colebrook Equation
 2.0 log
  
f
 3.7   Re f



f is not related explicitly Re and relative roughness in this equation.
The following equation can be used instead
f 
1.325
    5.74 
  0.9  
ln 
  3.7 D  Re  
2
for 106 

D
 10 2 and 5000  Re  108
Moody’s chart for friction factor
 /D
f
Laminar
Transition
f=64/Re
ReD
Increases
Minor Losses
Valves
Bends
T joints
hlm
Expansions
Contractions
V2
K
2g
• Flow separation and associated viscous effects will tend to decrease
the flow energy and hence the losses
• The phenomenon is fairly complicated. Loss coefficient ‘K’ will take
care of this complicities
Experiment 5 - New Experimental Set up
H
Reservoir
Digital Manometer
To measure ΔP
Experiment 5 - Experimental Steps & Details
Overall Measurements
H
1. Measure the Reservoir Height, H
2. Measure the Distances L1, L2, etc.
3. Measure the distances Δx1, Δx2, etc. Measure the pipe diameters
Reservoir
L1
For EACH PIPE Follow Steps below
L2
L3
L4
Δx2
•
Δx1
Set the reservoir height, H, to the maximum level, approx. close to the ‘spill-over’
partition height. Record the level. Δx2
• Adjust the flow rate to a relatively high value, wait for steady flow to be
established.
Δx3
1. Measure the flow rate.
2. Measure the pressure drop, ΔP, for this flow rate.
3. Reduce the flow rate, by using the valves, repeat steps 1 & 2.
4. Reduce the reservoir height and repeat steps 1-3.
5. Repeat all steps until 3 reservoir heights have been measured
Hence for each pipe, you will measure ΔP, for six flow rates
(3 H x 2 valve openings)