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2500 solved problems in fluid mechanics hydraulics - 341

330

0 CHAPTER 13
W ater flows through the piping system shown in Fig. 13-8 with certain measured flows indicated on the sketch. D etermine the flows throughout the network. Use C = 120 throughout.

13.8

I
Hne
AB BE EF FA

D,m
20 16 16 24

L,

ft

assumed Q i , «ngd 4.0 1.0 -2.0 -6.0

s,
ft/1000 ft

LH L H, ft 4.86 1.48 -3.99 -5.64
Qi
A

Qi

3000 4000 3000 4000

1.62 0.37 -1.33 -1.41

1.22 1.48 2.00 0.94 5.64 0.95 2.66 6.30 1.48 11.39 2.00 5.92 2.00 4.85 14.77 6.30 5.92 4.44 5.92 22.58

+ 0.31 + 0 . 3 1 - ( 0 . 1 3 ) = +0.18 +0.31-(0.50) = -0.19 + 0.31

4.31 1.18 - 2.19 - 5.69

E = - 3.29
BC CD DE EB

20 16 12 16

3000 4000 3000 4000

3.0 2.0 -1.5 -1.0

0.95 1.33 -3.15 -0.37

2.85 5.32 -9.45 -1.48

+ 0.13 + 0.13 + 0 . 1 3 - ( - 0 . 1 2 ) = +0.25 +0.13-(0.31) = -0.18

3.13 2.13 - 1.25 - 1.18

S = -2.76
FE EH HG GF

16 12 16 16

3000 4000 3000 4000

2.0 1.0 -2.0 -4.0

1.33 1.48 -1.33 -4.85

3.99 5.92 -3.99 - 19.40 E = - 13.48

+ 0 . 5 0 - ( + 0 . 3 1 ) = +0.19 + 0 . 5 0 - ( - 0 . 1 2 ) = +0.62 + 0.50 + 0.50

2.19 1.62 - 1.50 - 3.50

ED DI IH HE

12 12 12 12

3000 4000 3000 4000

1.5 1.0 -1.0 -1.0

3.15 1.48 -1.48 -1.48

9.45 5.92 -4.44 -5.92

-0.12-(0.13) = -0.25 -0.12 -0.12 -0.12-(0.50) = -0.62

1.25 0.88 - 1.12 - 1.62

E = + 5.01
A , = -(-3.29)/[1.85(5.64)] = +0.31 A = -(-13.48)/[1.85(14.77)] = +0.50
m m

A „ = -(-2.76)/[1.85(11.39)] = +0.13 A = -(+5.01)/[1.85(22.58)] = - 0 . 1 2
IV

F or line EFia l oop I, its net A term is (A, - A ) or [+0.31 - (+0.50)] = - 0 . 1 9 . It will be observed that the A for loop I is combined with that of the A for loop III since the line EF o ccurs in each loop. In similar fashion, for line F E i n loop III, the net A term is ( A - A ) o r [+0.50 - (+0.31)] = +0.19. Note that the net A's have t he same magnitude but opposite signs. This can readily be understood since flow in EF is counterclockwise for l oop I, whereas flow in FE in loop III is clockwise.
ra t

3 000'-20" 4 mgd

3000-20" 3 mgd

• 1 mgd

r
* F

is

1

s

io
2 mgd 3 000'-16"

F
G ^

II

1

o •v 1.5 mgd 3 000'-12" D

- 2.5 mgd

x

V

1!
r

m

l §

I , t| "v
H LMGÁ
R

G

2mgd_ 3 000'-J6"

3 000'-12" 2 mgd

2 mgd

V

Fig-13-8

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