Chapter (10) · 2013. 11. 6. · Equation (10.22) is called Darcy-Weisbach Equation 64 min :For La ar Flow f = R e 2 0 8 1 = R f − : log( ) . f For Turbulent Flow e. ... The problems

Dr. Munzer Ebaid Dr. Munzer Ebaid 11

Flow in conduits

SUMMARY

Chapter (10)

Dr. MUNZER EBAID

MECH. ENG. DEPT.


Shear Stress and Velocity Distribution across a Pipe Section

1. Shear Stress distribution is linear.

2. Velocity distribution is parabolic.


The Average Velocity

Laminar Flow in a Pipe

The Head Loss

The Discharge


Velocity Distribution in a Smooth Pipe for Turbulent Flow

Applicable everywhere except near the wall

Turbulent Flow in a Pipe


factorfrictioncalledisfwherefcf 4=

(m) varies from 1/6-1/10

Depending on Re


Equation (10.22) is called Darcy-Weisbach Equation

64eRfFlowarLaFor =:min

8021 .)(log: −= fRf

FlowTurbulentFor e


( ) .',,)( usedisdiagramsMoodyinplotD

KRHenceknownare

DK

andVWhen SeS ⎟

⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

( ) .',,)()( usedisdiagramsMoodyinplotD

KfRHenceknownare

DK

honlyandknownnotisVWhen SeS

f ⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛

Moody’s Diagram


Swamee & Jain Formula

%)(')(

)(

3

1021010104 2583

bydiagramsMoodyfromcediffererenfD

KandRFor Se

−− ×


SituationSituation Given ValuesGiven Values Computed Computed

Values in orderValues in orderValues Values

read from read from Moody's Moody's diagramdiagram

Final Value Final Value requiredrequired

Case (a)Case (a)

Case (b)Case (b)

Case (c)Case (c) Assume a value for , Assume a value for , then calculatethen calculate

Iterative Iterative procedure is procedure is used to computeused to compute

mLDKS &,,,

fS hLDK ,,,

LmhK fS ,,, &

DK

RV Se ,,

2123 2⎟⎠⎞

⎜⎝⎛

LghD

DK fS

ν,

f fh

QmV && ,,

DeS RVDK ,,⎟⎠⎞⎜⎝⎛)(D

eRf ,

eRf ,

The problems in the previous slide are summarized in the Table below:


Example (10.7)Case (C)To solve for the pipe size, i.e (D), an iterative procedure is followed as follows

Assume an initial value for (f)

f D Vk/D Re New (f)Compare (f) with New (f)


Explicit Equations for Discharge (Q) and Diameter (D)

Swamee & Jain Formula

Streeter & Wile

mLDKS &,,, To calculateGiven fh


Loss Coefficients For Various Transition and Fittings


Transition Losses and Grade Lines Energy Grade Line

Hydraulic Grade Line


Pipe SystemsSimple Pump in a

Pipe Systems


Pipe in Parallel


Pipe Networks

S = Sources

L = Loads

The requirements of the pipe

networks design are:

1. Layout of the pipes.

1. Pipe sizes.

2. Future loads.

For the design of the pipe networks,two conditions must be satisfied:

1. Continuity must be satisfied.2. Head loss between any two junctions must

be the same.

DCACBCAB

DCACBCAB

hhhhConditionQQQQCondition

+=++=+

:)(:)(

21


Uniform Free – Surface Flows

500eRFlowTurbulentFor :

2000/4=500

3000/4=750


Rock – Bedded Channels

Example (10.16)


The Chezy Equation and Manning Equation

Manning Eqn.(SI units)

n= The Manning’s Number

Chezy Equation

Manning Eqn.(Imperial units)


Best Hydraulic Section

The best hydraulic section is the channel proportion that yields a minimum wetted perimeter for a given cross section, hence a large discharge.

factortionthecalledisPAAARtermThe h sec

3232 ⎟

⎠⎞

⎜⎝⎛=

PQandAQthatseenbecanIt 1αα(

For a given channel (hence resistance) and a slope


Best Hydraulic Section

1. Trapezoidal channel=1/2 a hexagon

2. Circular channel=1/2 a Circle

3. Triangular channel=1/2 a square

Uniform Flow in Culverts and Sewers

Conditions for Design of Sewers:

1. Maximum flow condition.

2. Minimum velocity = 2 ft/s (0.60 m/s).


Uniform Flow in Culverts

A Culvert is a conduit placed under a fill such as highway embracement. It is used to convey stream flow from uphill side of the fill to the downhill side.


END OF SUMMARY

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Chapter (10) · 2013. 11. 6. · Equation (10.22) is called Darcy-Weisbach Equation 64 min :For La ar Flow f = R e 2 0 8 1 = R f − : log( ) . f For Turbulent Flow e. ... The problems