Experiment 5Pipe Flow-Major and Minor losses ( review)

• The goal is to study pressure losses due to viscous ( frictional) effects in fluid flows through pipes

Flow meter

Differential Pressure Gauge- measure ΔP

LValve

H

Reservoir

PipeD

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)

g

V

D

LfhEquationsDarcy l 2

'2

Due to wall friction Due to sudden expansion, contraction, fittings etc

g

VKhlm 2

2

K is loss coefficient must be determined for each situation

In this experiment you will find friction factor for various pipes

For Short pipes with multiple fittings, the minor losses are no longer “minor”!!

Major loss

• Physical problem is to relate pressure drop to fluid parameters and pipe geometry

Differential Pressure Gauge- measure ΔP

PipeD

V

L

ρ μ ε

),,,,,( DLVP

Using dimensional analysis we can show that

DD

LVD

V

P

,,

2

1 2

Friction factor

g

V

D

Lfh

g

P

VD

LfPor

VfD

LPie

D

VDffactorfrictiondefine

VD

VD

D

LP

D

VD

D

L

V

P

LL

L

2

2

1

2

1

,

2

1,

,

2

1

2

2

2

2

2

2

2

2

11

2

VL

DPf

g

V

D

Lfh

L

L

Friction Factor

• For Laminar flow ( Re<2300) inside a horizontal pipe, friction factor is independent of the surface roughness.

Df

D

VDf

Re,,

asiprelationshfunctionalthederivecanwellyTheoretica

onlyfie .Re

• 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

Re

64f For Laminar flow

Friction factor correlations

f is not related explicitly Re and relative roughness in this equation.

The following equation can be used instead

f

D

fEquationColebrook

Re

51.2

7.3

/log0.2

1

826

2

9.0

10Re50001010

Re

74.5

7.3ln

325.1

andD

for

D

f

Moody’s chart for friction factor

f

ReD

Laminar

f=64/Re

Tra

nsiti

on

Smooth

D/ Increases

Minor Losses

• 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

Valves Bends T joints Expansions Contractions

g

VKhlm 2

2

Experiment 5 - New Experimental Set up

H ReservoirDigital ManometerTo measure ΔP

Experiment 5 - Experimental Steps & Details

H ReservoirOverall Measurements1. Measure the Reservoir Height, H2. Measure the Distances L1, L2, etc.3. Measure the distances Δx1, Δx2, etc. Measure the pipe diameters

L1

L2

L3

L4

Δx2

Δx2

Δx3

For EACH PIPE Follow Steps below• Set the reservoir height, H, to the maximum level, approx. close to the ‘spill-over’

partition height. Record the level.• Adjust the flow rate to a relatively high value, wait for steady flow to be established.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 measuredHence for each pipe, you will measure ΔP, for six flow rates (3 H x 2 valve openings)

Δx1