Question

A pipe network is given below (Figure 2). All pipes are 1 km long, and 500 mm in diameter, with friction factor of 0 018 Determine the following. a) The value of Q (3) b) The correct flows in each pipe (using the Hardy-cross method) after the (17) first iteration [Hint: Assume Qo for pipe AB 105 L/s] c) The pressure heads at each node if the pressure head at reservoir A is 80 m. The elevation of each node is provided in Table 2 (7) Assume friction factor of 0 018 for all pipes Ignore all minor losses. X Table 2: 60 40L/s 30L/s Pipe Elevation A |(m) A 25 C 30 D 30 40L/s 50L/s 020 25 30 Figure 1. Pipe network (Q 4) 30

Answer 1

Ans a) According to figure,

0.60 Q = 0.20 Q + 40 + 30 + 50 + 40

=> Q = 400 L/s

Ans b) We know, accordin g to Hardy Cross Method,

H_L = K Q² , where, K = 8 f L / (g $\pi$² D⁵)

K = 8(0.018)(1000) / (9.81 x 3.14 x 0.5⁵)

= 47.64 for all pipes

Step 1 - Assume discharge in each pipe and asign a flow direction as shown below :

2404 A 12oL/8 A VYOLLS 120L/6 30L/8 yoL/s BOLIS SOL/S

We know, Q_correct = Q + $\Delta$ Q

where, $\Delta$ Q = - $\sum$H_L / 2 (H_L/Q)

Assume flow in clockwise direction as positive and vice versa ,

Loop ABCD,

Pipe	Q (L/s) / m3/s	K	HL (m)	HL/Q ( m /m3/s)
AB	120 / 0.12	47.64	0.68	5.667
BC	40 / 0.04	47.64	0.076	1.9
DC	-40 / -0.04	47.64	-0.076	-1.9
DA	-120 / -0.12	47.64	-0.68	-5.667

=> $\Delta$ Q = - $\sum$H_L / 2 (H_L/Q)

Here,  $\sum$H_L = 0

=> $\Delta$ Q = 0

=> Q_correct for pipe ;

AB = 120 L/s

BC = 40 L/s

DC = 40 L/s

AD = 120 L/s

Loop BEFC

Pipe	Q (L/s) / m3/s	K	HL (m)	HL/Q ( m /m3/s)
BE	40 / 0.04	47.64	0.076	1.90
EF	10 / 0.01	47.64	0.0047	4.70
CF	-30 / -0.03	47.64	-0.0428	1.427
BC	-40 / -0.04	47.64	-0.076	1.90

=> $\Delta$ Q = - $\sum$H_L / 2 (H_L/Q)

= - 0.0042/ 2(9.927)

= - 0.00021 m³/s or 0.21 L/s

=> Q_correct for pipe :

BE = 40 - 0.21 = 39.79 L/s

EF = 10 - 0.21 = 9.71 L/s

CF = - 30 - 0.21 = 30.21 L/s

BC = -40 - 0.21 = 40.21 L/s

Ans c) Following are the pressure head at each node

A -> 70 - 30 = 40 m

B = 31.26 m

C = 21.20 m

D = 28.56 m

E = 14.94 m

F = 38.54 m