Head Losses at Bends

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13. Pipe flow I (6.1-6.4, 6.6)

• Energy losses in pipe flow• Local energy losses• Pipes connected in series

Exercises: D13, D14, and (D15)

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PIPE FLOWFlow of water, oil and gas in pipes is of immense importance in civil engineering:• Distribution of water from source to consumers (private,

municipal, process industries)• Transport of waste water and storm water to recipient via

treatment plant• Transport of oil and gas from source to refineries (oil) or into

distribution networks (gas) via pipelines

Some data from Sweden:• Average water consumption: 330 liters/(person and day)• Purchase cost (“Anskaffningsvärde”) for water and waste

water pipes: 250 billion SEK• Length of all water pipes put together: 67000 km

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TWO FACTORS OF IMPORTANCE IN DESIGN OF PIPES

1) Hydraulic transport capacity of the pipeIn a pressurized system the hydraulic transport capacity is a function of the fall of pressure along the pipe. The fall of pressure is caused by energy losses in the pipe:- Energy losses due to friction due to shear stresses along pipe

walls - Local losses that arises at pipe bends, valves, enlargements,

contractions, etc

2) Strength of pipe – usually determined on basis of high and low pressures in conjunction with flow changes (closing of valve or pump stop)

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(trycknivå)(trycknivå)

(total energi)(total energi)

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ENERGY LOSSES IN PIPE FLOW

Energy equation:

The objective is to determine a relation between energy losses andmean velocity in a pipe:

hfriction = f(V) and hlocal = f’(V)

losseshg

Vz

p

g

Vz

p∑+++=++

2

22

22

2

21

11

γγ

localhfrictionhlossesh ∑+=∑

w w

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Energy losses due to frictionCalculated using Darcy – Weisbach’s formula(general friction formula for both laminar and turbulent flow; Eq. 6.12):

hf – energy loss due to friction over a distance, L (m), along the pipef – pipe friction factor [f=f(Re, ”Pipe wall roughness”); Fig. 6.10 –

Moody diagram, laminar flow → f = 64/Re; Re = VD/ν]D – Pipe diameter (m)V – average velocity in the pipe (m/s)Q – flowrate in the pipe (m3/s)

2

2

5

2

216

2 πgQ

DLfhor

gV

DLfh ff ==

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D13 Calculate the smallest reliable flowrate that can be pumped through this pipeline. D = 25 mm, f = 0.020, L = 2 x 45 m, Vertical distances are 7.5 m and 15 m respectively. Assume atmospheric pressure 101.3 kPa.

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Local energy losses

• Minor head losses in pipelines occur at pipe bends, valves (“ventiler”), enlargement and contraction of pipe sections, junctions (“knutpunkter”) etc.

• In long pipelines these local head losses are often minor in comparison with energy losses due to friction and may be neglected.

• In short pipes, however, they may be greater than frictional losses and should be accounted for.

• Local losses usually result from abrupt changes in velocity leading to eddy formation which extract energy from the mean flow.

• Increase of velocity is associated with small head (energy) losses and decrease of velocity with large head losses

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Local energy losses (cont.)

Usually it is possible to write local energy losses in pipe flow using thefollowing formula:

hlocal = local energy lossKlocal = local loss coefficient (different for different types of losses)V2/(2g) = kinetic energy (velocity head)

g

VlocalKlocalh

2

2⋅=

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LOCAL ENERGY LOSS - ENLARGEMENT

:

D2/D1

1.5 2.0 2.5 5 10

KL 0.31 0.56 0.71 0.92 0.98

Loss coefficient, KL, for sudden enlargement (V=V1):

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ENERGY LOSS FOR OUTFLOW IN RESERVOIR

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LOCAL ENERGY LOSS - CONTRACTION

Loss coefficientfor sudden contraction(Franzini and Finnemore, 1997, V = V2):

D2/D1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

KL 0.50 0.45 0.42 0.39 0.36 0.33 0.28 0.22 0.15 0.06 0.00

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Head loss coefficient for different types of pipeentrances

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Head loss at smooth pipe bends

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Loss coefficients at right angle bends

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Pipe systems – pipes in series

Solution• Energy equation ⇒ Total head, H = Δz = hf1 + hf2 + Σhlocal

• Continuity equation ⇒ Q = Q1 = Q2

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D14 Water is flowing. Calculate the gage reading when V300 is 2.4 m/s. (NOTE El. = elevation)

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D15 Calculate magnitude and direction of manometer reading.