Flow through pipes

Flow through Pipes•Characteristics of flow through pipes•Energy (head) losses in flow through pipes•Major losses such as loss of head due to friction Darcy Wisbachformula•Minor losses such as loss of head at entry, change in diameter, bend etc.•Problems on head losses•Hydraulic Gradient Line (H.G.L.) & Total Energy Line (T.E.L.)•Effect of entry at pipe, change in diameter, bend etc. on H.G.L. &•T.E.L.•Plotting of H.G.L. & T.E.L.•Design of pipeline for given flow --using formulae ---using nomograms•Computation of height of reservoir•Compound pipe and equivalent sizes

Where the fluid moves slowly in layers in a pipe, without much mixing

among the layers.

• Typically occurs when the velocity is low or the fluid is very viscous.

Laminar flow:

Turbulent flow

•Opposite of laminar, where considerable mixing occurs, velocities

are high.

•Laminar and Turbulent flows can be characterized and quantified

using Reynolds Number

•established by Osborne Reynold and is given as –

Laminar and Turbulent Flow Summary

• Laminar Flow Layers of water flow over one another at different speeds with virt

ually no mixing between layers. The flow velocity profile for laminar

flow in circular pipes is parabolic in shape, with a maximum flow in the

center of the pipe and a minimum flow at the pipe walls. The average

flow velocity is approximately one half of the maximum velocity.

• Turbulent FlowThe flow is characterized by the irregular movement of particles of the

fluid. The flow velocity profile for turbulent flow is fairly flat across the

center section of a pipe and drops rapidly extremely close to the walls.

The average flow velocity is approximately equal to the velocity at the

center of the pipe.

• Viscosity is the fluid property that measures the resistance of

the fluid to deforming due to a shear force.

For most fluids, temperature and viscosity are inversely

proportional.

http://www.ceb.cam.ac.uk/pages/mass-transport.html

• An ideal fluid is one that is incompressible and has no viscosity.

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Head Loss

• In the analysis of piping systems, pressure losses are

commonly expressed in terms of the equivalent fluid column

height called head loss hL.

• It also represents the additional height that the fluid needs to

be raised by a pump inorder to overcome the frictional losses

in the pipe

gd2

fLV

g

Ph

2

avgL

L

7

8

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Hagen – Poiseuille’s Law

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Friction Factor : Major losses

• Laminar flow

• Turbulent (Smooth, Transition, Rough)

• Colebrook Formula

• Moody diagram

• Swamee-Jain

Laminar Flow Friction Factor

Hagen-Poiseuille

Darcy-Weisbach

2

32

lhgDV

L

f 2

32 LVh

gD

2

f f2

L Vh

D g

g

V

D

L

gD

LV

2f

32 2

2

64 64f

ReVD

Slope of ___ on log-log plot-1

fh V

f independent of roughness!

4

128

lghDQ

l

Turbulent Flow:

Smooth, Rough, Transition • Hydraulically smooth

pipe law (von Karman, 1930)

• Rough pipe law

(von Karman, 1930)

• Transition function

for both smooth and

rough pipe laws (Colebrook)

2

f f2

L Vh

D g

1 Re f2log

2.51f

1 3.72log

f

D

1 2.512log

3.7f Re f

D

*

f

8u V (used to draw the Moody diagram)

Friction losses in Pipes

• Vary with laminar or turbulent flow

• Energy equation can be given as –

p1/γ + z1 + v12/2g + hA – hR – hL = p2/γ + z2 + v22/2g

• where hA, hR, hL are the heads associated with addition,

removal and friction loss in pipes, respectively.

• The head loss in pipes = hL can be expressed as

• Darcy’s equation for energy loss (GENERAL FORM)

Where

• f – friction factor

• L – length of pipe

• D – diameter of pipe

• v – velocity of flow

• Another equation was developed to compute hL under

Laminar flow conditions only

called the Hagen-Poiseuille equation

• If you equate Darcy’s equation and Hagen-Poiseuille equation

• Then we can find the friction factor f

Thus the friction factor is a

function of Reynold’s number!

Moody diagram

Moody Diagram that can be used to estimate friction coefficients

• The Moody friction factor - λ (or f) - is used in the Darcy-

Weisbach major loss equation

• If the flow is transient - 2300 < Re < 4000 - the flow varies

between laminar and turbulent flow and the friction coefficient

is not possible to determine.

• The friction factor can usually be interpolated between the

laminar value at Re = 2300 and the turbulent value at Re =

4000

• Moody diagram

DARCY WEISBACH EQUATION

• Weisbach first proposed the equation we now know as the

Darcy-Weisbach formula or Darcy-Weisbach equation:

• hf = f (L/D) x (v2/2g)

where: hf = head loss (m)

• f = friction factor L = length of pipe work (m) d = inner

diameter of pipe work (m) v = velocity of fluid (m/s) g =

acceleration due to gravity (m/s²)

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Minor Losses

• Piping systems include fittings, valves, bends, elbows, tees,

inlets, exits, enlargements, and contractions.

• These components interrupt the smooth flow of fluid and

cause additional losses because of flow separation and mixing.

• The minor losses associated with these components:

KL is the loss coefficient.

• Is different for different components.

• Typically provided by manufacturers.

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• Total head loss in a system is comprised of major losses (in

the pipe sections) and the minor losses (in the components)

• If the entire piping system has a constant diameter, then

i pipe sections j components

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Laminar flow

Laminar Boundary Layer Flow

• The laminar boundary layer is a very smooth flow, while the

turbulent boundary layer contains swirls or “eddies.”

• The laminar flow creates less skin friction drag than the

turbulent flow, but is less stable.

• Boundary layer flow over a wing surface begins as a smooth

laminar flow. As the flow continues back from the leading

edge, the laminar boundary layer increases in thickness.

Turbulent Boundary Layer Flow

• At some distance back from the leading edge, the smooth

laminar flow breaks down and transitions to a turbulent flow.

• From a drag standpoint, it is advisable to have the transition

from laminar to turbulent flow as far aft on the wing as

possible, or have a large amount of the wing surface within the

laminar portion of the boundary layer.

• The low energy laminar flow, however, tends to break down

more suddenly than the turbulent layer.

– Pipes in series is defined as the pipes of different lengths and different diameters connected end to end to form a pipe line.

L1,L2,L3 = length of pipes 1,2 and 3

d1,d2,d3 = diameter of pipes 1,2,3

v1,v2,v3 = velocity of flow through pipes 1,2,3

f1,f2,f3 = coefficient of frictions for pipes 1,2,3

H = difference of water level in the two tanks

The discharge passing through the pipe is same.

Q=A1V1=A2V2=A3V3

– The difference in liquid surface levels is equal to the sum of the total head loss in the pipes

Flow through the pipes in series

Parallel pipe system

• Consider a main pipe which divide into two or more branches as

shown in figure

Again join together downstream to form a single pipe then the branch

pipes are said to be connected in parallel. The discharge through the

main is increased by connecting pipes in parallelthe rate of flow in the

main pipe is equal to the sum of rate of flow through branch pipes.

hence Q =Q1+ Q2

• In this arrangement loss of head for each pipe is same

Loss of head for branch pipe1=loss of head for branch pipe 2

Total energy gradient line

• Total energy gradient line is equal to sum of

pressure head ,velocity head and datum head

EL = H = p / W + v2 / 2 g + h = constant along a streamline

where

(EL ) Energy Line

• For a fluid flow without any losses due to friction (major losses) or components (minor losses) - the energy line would be at a constant level. In a practical world the energy line decreases along the flow due to losses.

• A turbine in the flow reduces the energy line and a pump or fan in the line increases the energy line

Hydraulic Grade Line (HGL )

• Hydraulic gradient line is the sum of pressure head and datum

head

HGL = p / W + h

where

The hydraulic grade line lies one velocity head below the

energy line.