Friction losses in Expansion, Contraction

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Friction losses in Expansion, Contraction Pipe
Fittings

• Friction losses in flow thro straight pipe are
  calculated by using Fanning friction factor f
• If the velocity of the fluid is changed in
  direction or magnitude, additional friction
  losses occur.
• This results from additional turbulence which
  develops becz of vortices and other factors.
• Sudden enlargement losses
• Sudden contraction losses
• Losses in fittings and valves

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• Sudden enlargement losses
• Sudden contraction losses
• Losses in fittings and valves

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• We know Bernoullis eqn
• Total friction losses to be used in Bernoullis
  equation

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Prob 2

• An elevated storage tank contains water at 82.2C
  as shown in Fig. It is desired to have a
  discharge rate at point 2 of 0.223ft3/s. What
  must be the height H in ft of the surface of the
  water in the tank relative to the discharge
  point? The pipe used is commercial steel pipe,
  schedule 40, and the lengths of the straight
  portions of pipe are shown.
• Density 0.97 g/cc viscosity 0.347 cP

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For Schedule 40 pipe, 4 4.026 2 2.067
and e 4.6x10-5m Kc 0.55 (for tank
4pipe) Kf 0.75 (4elbow 2elbow) Kc 0.405
(4 2 pipe)
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• Contraction loss _at_ tank exit
• Friction in 4 pipe
• Friction in 4 elbow
• Contraction loss from 4 to 2 pipe
• Friction in 2 pipe
• Friction in the two 2 elbow

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• v3 (0.223 ft3 /sec) / CSA of 4 pipe
• 0.7688 m/sec
• v4 v2 (0.223 ft3 /sec) / CSA of 2 pipe
• 2.9168 m/sec

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• Contraction loss _at_ tank exit
• Friction in 4 pipe

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• Friction in 4 elbow
• 4. Contraction loss from 4 to 2 pipe

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• Friction in 2 pipe

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• 6. Friction in the two 2 elbow

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• p1 p2
• v1ltltv2

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Prob 3

• Water _at_ 20ºC is being pumped from a tank at the
  rate of 5x10-3 m3/s. All of the piping is 4
  schedule 40 pipe. The pump has an efficiency of
  65. Calculate the kW power needed for the pump.
• Givenfor 4 Schedule 40 pipe, D0.1023m
• Kc0.55 Density 998.2 kg/m3
• Kf0.75 Viscosity1.005 cP
• Kex1.0

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• Frictional losses are..
• Contraction loss _at_ tank exit
• Friction in straight pipe
• Friction in the two elbows
• Expansion loss _at_ tank entrance
• Velocity (5x10-3 ) / CSA 0.6083 m/s

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1. Contraction loss _at_ tank exit
2. Friction in straight pipeMOODY chart.ppt
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3. Friction in the two elbows

• Total losses 6.837 J/kg

4. Expansion loss _at_ tank entrance
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• By Bernoullis eqn

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EQUIVALENT LENGTH

• In some applications it is convenient to
  calculate pressure drops in fittings from added
  equivalent lengths of straight pipe
• Le is the equivalent length of st. pipe in m
  having the same frictional loss as the fitting.
• The Le values for fittings are simply added to
  length of the st. pipe to get the total length of
  equivalent st. pipe to use in (FL)

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• Water _at_ 20ºC is pumped from a storage tank thro
  100m of
• 3cm dia pipe. The pipe line has TWO globe valves
  which
• are fully open and THREE 90º elbows. Water is
  discharged
• into another tank thro a spray nozzle. The
  discharge is _at_ a
• height of 20m above the level of water in the
  storage tank.
• The pressure required _at_ the nozzle entrance is
  4x105
• N/m2. Flow rate of water 1kg/sec. Viscosity is
  0.975 cP
• f 0.0014 0.125/Re0.32
• Estimate a). Energy loss due to fricition
• b). Pump work required per kg of water
• c). Theoretical HP required for the pump
• Equivalent length in terms of pipe dia
• Open globe valve 300D
• 90ºElbow 30D

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• V 1.4147 m/sec
• NRe 43 529.55
• f 0.00549
• To calculate FL)T first find total length L.
• L L Le 100 (2x300x0.03) (3x30x0.03)
  120.7 m
• 2 f L v2 / D 88.413 J/kg
• Sub. in Bernoullis eqn.assume Pa 1 atm
• Wp 585.617 J/kg
• ? 0.786HP

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• Water is to be pumped from a pond to the top of a
  tower 1829cm above the water level in the pond.
  It is desired to deliver 0.34 cu m/min of water
  at a pressure of 2.08atm. The pipe line consists
  of 122m length of st. pipe of 7.62cm ID with
  EIGHT elbows of 90º FOUR gate valves.
  Calculate the HP of the pump having an efficiency
  of 80
• f 0.046 / Re0.2
• Equivalent length in terms of pipe dia
• Gate valve 7D
• 90ºElbow 32D

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• V 1.2425 m/sec
• NRe 90 957.58
• f 0.004688
• To calculate FL)T first find total length L.
• L L Le 122 (8x32x0.0762)
  (4x7x0.0762) 143.64 m
• FL)T 2 f L v2 / D 27.239 J/kg
• Sub. in Bernoullis eqn.assume Pa 1 atm
• Wp 394.29 J/kg
• ? 2.999HP

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Flow in non-circular ducts

• For flow in a duct of non-circular cross-section,
  the hydraulic mean diameter may be used in place
  of the pipe diameter and the formulae for
  circular pipes can then be applied without
  introducing a large error. This method of
  approach is entirely empirical.
• The hydraulic mean diameter DH is defined as four
  times the hydraulic mean radius rH.
• Hydraulic mean radius is defined as the flow
  cross-sectional area divided by the wetted
  perimeter.
• rH (cross sectional area of channel) /
  (wetted perimeter of channel)

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Few Examples

• For circular tube.
• Annulus between two concentric pipes
• For square duct.
• For rectangular duct..

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prob1

• a). Calculate the hydraulic mean diameter of the
  annular space between a 40mm and a 50mm tube.
• b). A liquid having a density of 60.58lb/ft3 and
  a viscosity of 0.347cP is flowing thro a pipe of
  dia 0.3355ft. The flow rate of the liquid is
  75cm/sec. Calculate the Reynolds number.

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• A horizontally placed pipe carries fluid (sp.gr.
  0.983 and viscosity 8.35cP) at a mass flow rate
  of 50kg/s/. Besides the pipe friction there is a
  flow restriction in the pipe whose frictional
  resistance can be expressed as HR 4.65V metres
  of fluid where V is the ave.linear velocity of
  the fluid in m/s. The friction factor in the pipe
  is given by
• f0.073/NRe0.226
• If the internal dia of pipe is 45cm and its
  length is 4000m, calculate the total flow
  resistance developed during flow, expressed as
  metres of the flowing liquid

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• 60 sulfuric acid is to be pumped at the rate of
  4000cc/sec thro a pipe 25mm dia and raised to a
  height of 25m. The pipe is 30m long and it runs
  straight. Calculate the theoretical power
  required.
• The sp.gr of the acid is 1.531. Friction factor
  may be assumed to be 0.0047
• 2.08 HP

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• Water at a rate of 200tons/hr has to be pumped
  from a river to factory overhead tank placed at a
  height of 25m from the river bed the total
  length of pipeline is 1.5km. Cast iron pipe
  having an ID of 30cm will be used for the
  purpose. The average temperature of water in the
  river may be taken as 30ºC, viscosity 0.764cP
• Cal Re
• Head lost due to friction
• Re 3x105
• f 0.0036
• h 2.255m

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• Its planned to install a steel pipe with an ID of
  20cm to transfer 1000kg/m3, molasses having a
  viscosity 500cP and density 1.6g/cc. The line is
  to be 1000m long and delivery end is to be 5m
  higher than the intake. Calculate
• Pressure drop due to friction
• If overall efficiency of the pump is 60 what
  will be the HP required?
• v 0.33157 m/s
• Re 212.2
• f 0.0754
• (FL)T 82.899 J/kg
• Wp 219.99 J/kg? 4.92HP

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• Determine the cost of pumping 3,00,000L/hr of an
  oil, sp.gravity 0.9 and viscosity 30cP thro a
  pipeline, 25cm dia and 50km long. It may be
  assumed that the efficiency of pump together with
  motor is 50 and the power costs 40paise/kW. The
  pipe line is horizontal and f 0.046/Re0.20
• v 1.697m/s
• Re 12,732
• f 6.946x10-3
• FL)T 8002.017 J/kg
• Wp 16006.91 J/kg
• ?Wp 1200.518kW
• Therefore cost Rs.480/-

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ASSIGNMENT - II

• Write short notes on following
• Boundary layer formation
• Boundary layer separation
• Drag coefficient
• Stream lining
• Entry length calculation
• Fully developed flow
• Last date of submission 21th April

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ASSIGNMENT - III

• Write short notes on following
• Positive displacement pumps
• Rotary pumps
• Airlift pumps
• Jet pumps
• Fans, blowers and compressors
• Different types of pipe fittings and valves
• Last date of submission 7th May