SAB2513 Hydraulic Chapter 7

7/31/2019 SAB2513 Hydraulic Chapter 7

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Introduction Water distribution network analysis provides the basis for the

design of new systems and extension of existing systems.

The design criteria are that specified minimum flow rates andpressure head~ must be attained at the outflow points of the

network.

The flow and pressure distributions across a network areaffected by the arrangements and sizes of the pipes and the

distribution of outflows.


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The flow in any network, however complicated, must satisfythe basic relations of continuity and energy as follows:

(a) The algebraic sum of flow rates in the pipes meeting at a

junction is zero

outin QQ

Introduction


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(b) The flow in each pipe must satisfy the pipe-friction laws (Darcy-Weisbach, Hazen-William, etc) for flow in a single pipe.

(c) The algebraic sum of the head losses in the pipe, around any closed loopformed by pipes, is zero

0f

h

n

fkQh


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Hardy Cross Method

2 solutions:(1) Balancing Head ----- Assume Q


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(2) Balancing Flow ----- Assume hf


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(i) At a junction:

(ii) Equation for head loss due to friction, hf:

(k and n values depend on the eqn used (Darcy-

Weisbach, Hazen-William, etc)

outin QQ

n

f kQh


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(a) Darcy-Weisbach Eqn.

(b) Blasius Eqn.

g

v

d

fLhf

2

42

,3

2

5Q

d

fL 2n

,1253

75.1

75.4Q

dLhf ,

125375.4

dLk 75.1n

53d

fLk


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(c) Hazen-William Eqn.

Where;

CHW = Hazen-William roughness coef.

(refer Table)

85.1

87.4

67.10Q

dC

fLh

HW

f

85.1n

87.4

67.10

dC

fLk

HW

Pipe Material CHWPlastic, PYC 150

Asbestos Cement 140

Welded Steel 120

Riveted Steel 110Concrete 130

Asphalted Iron -

Galvanised Iron -

Cast Iron (New) 130

Cast Iron (Old) 100Corrugated Metal -

Table: Hazen-Williams Coefficient,

CHW for different types of pipe


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1. Balancing Head Method

Applicable if the followings are known:

(i) Pipe characteristics such as diameter (d), Length (L)

and friction factor (f)

(ii) Qin, Qout in the system

Where discharges and pressure head are to be

determined????


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Balancing Head Method

Procedures:(i) Label the pipe network into close loops

(ii) Assumed values of Q in each pipe, but make sure:

at any junction: , where

(iii) Depending on the head losses eqn. used, calculate

hf for each pipe, i.e

(Note: sign for hf follows the sign for Q)

0Q outin QQ

n

f kQh


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(iv) For any loop: 0f

h


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Example:

0 fh


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(v) Calculate hf for each pipe in each loop (circuit)

(vi) For each loop/circuit, calculate the value of

(vii) Compute the error, Q:

(Note: n = 2 for Darcy-Weisbach eqn. &

n = 1.85 for Hazen-Williams eqn.)

Q

nhf

Q

nh

hQ

f

f


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Figure below shows layout of pipe network for a

water supply system. Determine the flow rate in

each pipe in the network by using Darcy-

Weisbach approximations.

(Note: assume that friction factor, f = 0.0025 for

all pipes)

Example


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17

Pipe Network

Pipe data


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Solution

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- Initial assumption for values and directions of Q

in each pipes- (Note: At a junction, Qin = Qout)


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Solution

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Equations to be used:

(i) Darcy-Weisbach eqn.

(ii)

(iii)

Construct the Table!!!

2

53

f

fLh Q

d

Q

hhQ

f

f

2

QQQ


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Solution

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Loop Trial 1

1

pipe d(m) L(m) k=fL/3d5 Q1 hf=kQ12 2hf/Q1 Q1 Q= Q1+Q1

AB 0.5 1000 26.666 0.2 1.0667 10.667 -0.0783 0.1217

AC 0.75 1200 4.2140 -0.3 -0.3793 2.5284 -0.0783 -0.3783

BC 0.5 1500 40.00 0.2 1.600 16.000 0.0581 0.2581

Total, 2.2874 29.1951

0783.01951.292874.2

2

1

1

Q

hhQ

f

f


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Solution

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Loop Trial 2

2


BC 0.5 1500 40.000 -0.2 -1.6000 16.000 -0.0581 -0.2581

BD 0.25 1000 853.33 0.3 76.800 512.000 -0.1364 0.1636

CD 0.5 700 18.667 -0.3 -1.6800 11.200 -0.1364 -0.4364

Total, 73.52 539.2

1364.02.539

52.732

1

1

Q

hhQ

f

f


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Solution

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Loop Trial 2

1


AB 0.5 1000 26.666 0.1217 0.3946 6.4880 -0.0810 0.0407

AC 0.75 1200 4.2140 -0.3783 -0.6031 3.1883 -0.0810 -0.4593

BC 0.5 1500 40.00 0.2581 2.6440 20.6440 -0.0283 0.2297

Total, 2.4542 30.3164

0810.03164.304542.2

2

2

2

Q

hhQ

f

f


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Solution

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Loop Trial 2

2


BC 0.5 1500 40.000 -0.2581 -2.6636 20.6440 0.0284 -0.2297

BD 0.25 1000 853.33 0.1636 22.8534 279.2957 -0.0526 0.1110

CD 0.5 700 18.667 -0.4364 -3.5550 16.2923 -0.0526 -0.4890

Total, 16.6348 316.2320

0526.02320.3166348.16

2

2

2

Q

hhQ

f

f


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24


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Solution

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- Result: (Check the continuity at every junction),

Qin = Qout)


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2. Balancing Flow Method

When pressure head at a point in pipe network is known.

But the flow rates/discharges and pressure head at other

points in the network are to be determined


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(iv) Calculate value for each pipe then determine

the value of

(v) For correction purposes, calculate:

(vi) Recalculate the value of new head at J:

(vii) Repeat the procedures until

f

f

nh

Q

Q

h

fjj hHH

fnh

Q

fnh

Q

0 fh


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Using Darcy-Weisbach approximations, computeand sketch the flow distribution in the pipe network

below:

Example 3


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Solution

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Equations to be used:

(i) hf= difference of level between reservoir and junction J

(ii) Darcy-Weisbach eqn: where

(iii)

nf

k

hQ

1

2,

35

nd

fLk

f

f

nh

Q

Qh


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Solution

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(iv)

- Based on Principle of Flow

10 m < Hj < 50 m

- Assumption: Flow from A to B, C and D30 m < Hj < 50 m

Assume Hj = 35 m

Construct the Table!!!

fjj hHH


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Solution

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Trial 1

Hj = 35 m

pipe d(m) L(m) k=fL/3d5 hf1 Q1=(hf/k)1/2 Q1/(2hf1)

AJ 0.6 500 10.7167 15 1.1813 0.0394

BJ 0.3 1000 685.871 -5 -0.0584 0.0085

CJ 0.3 1500 1028.806 -25 -0.1559 0.0031

DJ 0.45 3000 270.9614 -15 -0.2353 0.0078

Total, 0.7065 0.0589

9884.110589.0

7065.0

1

f

h

9884.46)9884.11(35 J

H


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Solution

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Trial 2

Hj = 46.9884 m

pipe d(m) L(m) k=fL/3d5 hf2 Q2=(hf2/k)1/2 Q2/(2hf2)

AJ 0.6 500 10.7167 3.0116 0.5301 0.0880

BJ 0.3 1000 685.871 -16.9884 -0.1574 0.0046

CJ 0.3 1500 1028.806 -36.9984 -0.1898 0.0026

DJ 0.45 3000 270.9614 -26.9884 -0.3156 0.0058

Total, -0.1325 0.1011

3110.11011.0

)1325.0(

2

f

h

6774.453110.19884.46 JH


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Solution

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- Results (from table): after 4 trials

Check: At junction J:

(OK) Hj = 45.56 m

smQAJ /6436.03

,0Q

3070.01856.01506.06436.0 Q

smQBJ /1506.03

smQCJ /1856.03

smQDJ /3070.0

3

,0Q


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Solution

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SAB2513 Hydraulic Chapter 7

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