CBE 150A – Transport Spring Semester 2014 Other Friction Losses Valves and Fittings.

CBE 150A – Transport Spring Semester 2014

Other Friction LossesValves and Fittings


Goals

• Calculate frictional losses in a system Calculate frictional losses in a system containing valves, fittings, and sudden containing valves, fittings, and sudden expansions and contractionsexpansions and contractions

• Express frictional losses in terms of velocity Express frictional losses in terms of velocity head head

• Assess relative contributions of different Assess relative contributions of different sources to total viscous dissipationsources to total viscous dissipation


Sudden Expansion

Frictional losses occur as result of turbulence generated immediately downstream of the expansion


Sudden ExpansionAssume

2

2a

efe

VKh

Ke is the expansion loss coefficient which we will attempt to describe in terms of flow properties.


Sudden ExpansionMass Balance

bbbaaa SVSV

b

aab S

SVV


Sudden ExpansionMomentum Balance

gwbbbaaabb FFSpSpVVm 0 0

Assume turbulent: 12

Replaced Sa with Sb because pa is at the point of expansion.


Momentum Balance

abbab VVmppS

abb

VVSmp

abb VVV

bab VVV 2


Mechanical Energy Balance

f

abaabb h

ppzgVVW

22

2

1ˆ

Assume turbulent: 12

0 0

pVV

ppVVh

ba

babaf

2

222

22


Combining

babba

f VVVVV

h

222 1

2

2

2

2

2

22

ba

bbaa

VV

VVVV


Final Result

Recall Mass Balance Result:b

aab S

SVV

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

21

22

a

b

af

V

S

Sh


For Tank Filling

abb

a SSforS

S

11

0.12

2

ea

f KV

h

Sa

Va

Sb


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.


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.

2

2b

cfc

VKh

For laminar flow experimentally, Kc < 0.1 and hfc is usually neglected

a

bc S

SK 14.0Turbulent (empirical):

Note: Calculations again based on small cross section.


Tank Emptying

Sb

baa

b SSforS

S

11

4.02

4.02

c

bf K

Vh

Vb

Sa


Velocity Heads

2

42V

KKKD

Lfzzg

ppfecba

ba

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.

61 GlobeTee KK


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.

24

2V

D

Lfh total

f

Note: The values in the table are L/D and must be multiplied by D to get equivalent lengths.


Example

a

e

cTank 1

L2=10 ft5” Sch. 40 Steel

Pe = 30 psig

Tank 2d

b

L2=90 ft4” Sch. 40 Steel

∆Zab = -10 ft

∆Zbc = +0.5 ft

∆Zcd = +75 ft

∆Zde = +15 ft

gate valve (open)

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%.

Pa = 0 psig


0045.0

00036.0

12047.500015.0

/00015.0

1056.1107197.6

4.620.412047.5

0.41390.0

1

48.760

min1

min250

5

4

3

2

3

"5

f

ft

ftDkk

sftlb

ftlb

sft

ft

N

s

ft

ftgal

ft

s

galV

m

m

RE


0042.0

00045.0

12026.400015.0

/00015.0

1096.1107197.6

4.623.612026.4

3.60884.0

1

48.760

min1

min250

5

4

3

2

3

"4

f

ft

ftDkk

sftlb

ftlb

sft

ft

N

s

ft

ftgal

ft

s

galV

m

m

RE


m

f

f

m

f

cf

m

f

f

m

f

cf

pfcc

ae

lb

lbft

ft

ft

slb

lbft

sft

h

ansionfittingsD

Lf

g

Vh

lb

lbft

ft

ft

slb

lbft

sft

h

ncontractiofittingsD

Lf

g

Vh

Whg

zg

g

VPP

423.40.117.075.02

12026.4

)90(0042.04

2.322

3.6

exp4

2

206.04.00

12047.5

)10(0045.04

2.322

0.4

4

2

2

2

2

"4

2

"4

2

2

"5

2

"5

2


Hp

Hps

lbftlb

lbft

s

lb

P

s

lb

gal

lb

s

galm

Wlb

lbft

Wlb

lbftft

ft

lbftin

in

lb

Whg

zgP

f

m

fm

mm

pm

f

pm

f

m

f

pfc

e

9.13)70.0(550

4.15471.34

71.3433.8

60

min

min250

4.154

629.415755.0104.62

14430

3

2

2

2


10 Minute Problem

The Alaskan pipeline is 48 in. ID, 800 miles long and carries crude The Alaskan pipeline is 48 in. ID, 800 miles long and carries crude oil at a rate of 1.2 million bbl/day (1 bbl = 42 gallons). Assuming oil at a rate of 1.2 million bbl/day (1 bbl = 42 gallons). Assuming North Slope crude oil to be a Newtonian fluid with a viscosity of 25 North Slope crude oil to be a Newtonian fluid with a viscosity of 25 cP and a specific gravity of 0.87, what total pumping horsepower is cP and a specific gravity of 0.87, what total pumping horsepower is required to operate the pipeline ? The oil enters and leaves the required to operate the pipeline ? The oil enters and leaves the pipeline at sea level and the line contains the equivalent of 150 – 90 pipeline at sea level and the line contains the equivalent of 150 – 90 degree elbows and 100 fully open gate valves. degree elbows and 100 fully open gate valves.

Assume inlet and discharge pressures are equal to 1 atm.Assume inlet and discharge pressures are equal to 1 atm.

CBE 150A – Transport Spring Semester 2014 Other Friction Losses Valves and Fittings.

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Transcript of CBE 150A – Transport Spring Semester 2014 Other Friction Losses Valves and Fittings.