VVR 120 Fluid Mechanics

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

VVR 120 Fluid Mechanics

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

VVR 120 Fluid Mechanics

TWO FACTORS OF IMPORTANCE IN DESIGN

OF PIPES

1) Hydraulic transport capacity of the pipe

In 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)

VVR 120 Fluid Mechanics

(trycknivå)

(total energi)

VVR 120 Fluid Mechanics

ENERGY LOSSES IN PIPE FLOW

Energy equation:

The objective is to determine a relation between energy losses and

mean velocity in a pipe:

hfriction = f(V) and hlocal = f’(V)

losseshg

Vz

p

g

Vz

p

2

22

22

2

21

11

localhfrictionhlossesh

w w

VVR 120 Fluid Mechanics

Energy losses due to friction

Calculated 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 pipe

f – 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

2

16

2 g

Q

D

Lfhor

g

V

D

Lfh ff

VVR 120 Fluid Mechanics

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.

2

1

VVR 120 Fluid Mechanics

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

VVR 120 Fluid Mechanics

Local energy losses (cont.)

Usually it is possible to write local energy losses in pipe flow using the

following formula:

hlocal = local energy loss

Klocal = local loss coefficient (different for different types of losses)

V2/(2g) = kinetic energy (velocity head)

g

V

localKlocalh2

2

VVR 120 Fluid Mechanics

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):

VVR 120 Fluid Mechanics

ENERGY LOSS FOR OUTFLOW IN RESERVOIR

VVR 120 Fluid Mechanics

LOCAL ENERGY LOSS - CONTRACTION

Loss coefficient

for 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

VVR 120 Fluid Mechanics

Head loss coefficient for different types of pipe

entrances

VVR 120 Fluid Mechanics

Head loss at smooth pipe bends

VVR 120 Fluid Mechanics

Loss coefficients at right angle bends

VVR 120 Fluid Mechanics

VVR 120 Fluid Mechanics

Pipe systems – pipes in series

Solution

• Energy equation Total head, H = z = hf1 + hf2 + hlocal

• Continuity equation Q = Q1 = Q2

VVR 120 Fluid Mechanics

D14 Water is flowing. Calculate the gage reading

when V300 is 2.4 m/s. (NOTE El. = elevation)

2

1

VVR 120 Fluid Mechanics

D15 Calculate magnitude and direction of

manometer reading.