Page 194 - Water Engineering Hydraulics, Distribution and Treatment

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Water Hydraulics, Transmission, and Appurtenances
Chapter 5
PROBLEMS/QUESTIONS
A. Pipe diameters are 5, 4, and 2.5 cm as indicated in the figure
2
3
(g = 9.8m∕s ; = 1gm∕cm ; f = 0.0196).
A water supply system is shown in Fig. 5.27. The values of
5.1
(a) With C closed off and D freely flowing, determine the total
2
(
)
are indicated in the figure. The total discharge rate
K in h = KQ
f
static head required at A for a flow of 2.64 L/s at D.
3
from the system is 9 ft /s (255 L/s). The residual pressure at point
C is to be maintained at 20 psi (139 kPa). Find
the maximum quantity of water that can be provided at point C
(a) The flow rate in each pipe
before any water starts to flow out at D.
(b) The elevation of water surface in the reservoir
(c) The pressures at A, B, and E
D
L = 200 m
L = 300 m
D = 4 cm
B
EI. = 105 ft
Plan view
A
L = 100 m
C
D = 5 cm
D K = 0.08 A EI. = 90 ft (b) With both points C and D open to the atmosphere, determine
D = 2.5 cm
EI. = 90 ft
EI. = 110 ft K = 0.03
B Figure 5.29 Water system for Problem 5.3.
Water F E K = 0.08
reservoir EI. = 100 ft
K = 0.01 C 5.4 The elevation of a city distribution reservoir is 400 ft (122 m)
K = 0.20 and that of the city is 250 ft (76 m). When city water consumption
3
is at the rate of 16 ft /s (453 L/s), the pressure in the city is 60 psi
Figure 5.27 Water system for Problem 5.1. Conversion factor: (416 kPa).
1ft = 0.3048 m. Assuming that during a fire the minimum required pressure is
20 psi (139 kPa), determine the fire flow available if the coincidental
3
5.2 A village is investigating a new water supply plan. The supply city demand is 14 ft /s (396 L/s). (Neglect velocity heads and the
variation of f with Reynolds number.)
is to consist of a dam impounding water at A, from which it must
be pumped over a summit at B. From B it runs by gravity to the
village at D (see Fig. 5.28). Since the head available at the village is 5.5 Given the system shown in Fig. 5.30 and neglecting minor
more than would be used, putting in a hydroelectric plant at C has losses, velocity heads, and the variation of f with Reynolds number:
been suggested. The electric power will be transmitted back to the (a) What will be the flow rate from A to D if the pressure at D is to
pumping station and used for pumping water up to B. be maintained at 20 psi (139 kPa)?
Assume the following efficiencies: turbine 80%, generator
(b) What will the rate of flow be if the water level in reservoir A
90%, transmission line 95%, pump motor 80%, pump 75%. If the drops 10 ft (3 m), that is, to El. 170 ft (51.8 m)?
3
rate of water use is to be 6.28 ft /s (178 L/s), determine the excess
water horsepower still available at C. (c) What size of ductile iron pipe (f = 0.020) is required to carry
3
an additional 22 ft /s (623 L/s) from A to D with the reservoir
EI. 1,400 ft at 180 ft (55 m) and residual pressure at D to be maintained at
L = 10,000 ft L = 2,000 ft 20 psi (139 kPa)?
D = 2 ft B D = 2 ft
f = 0.03 f = 0.03
El. 180 ft
EI. 1,200 ft
A
A
Power Turbine and
transmission generator
P
line
Pump 18" d – 2,000' – f 0.025
C EI. 800 ft 18" d – 1,500' – f 0.030 El. 100 ft
To 18" d–1,000'– f 0.025
D village B C D
16" d – 1,500' – f 0.020
Figure 5.28 Water system for Problem 5.2. Conversion factor: Figure 5.30 Water system for Problem 5.5. Conversion factors:
′
′′
1ft = 0.3048 m. 1 = 1ft = 0.3048 m; 1 = 1in. = 25.4 mm.
5.3 In the sketch shown in Fig. 5.29, C and D represent points 5.6 A pipe 2 ft (600 mm) in diameter and 3 mi (4.83 km) long
on a university campus that are connected to a common junction connects two reservoirs. Water flows through it at a velocity of 5 ft/s
B through 100 and 200 m lengths of pipe, respectively. Points B (1.5 m/s). To increase the flow, a pipe 1.5 ft (450 mm) in diameter
and C are on the lower level of campus at elevation of 12 and is laid parallel alongside the first pipe for the last mile.
6 m, respectively, above mean sea level (MSL), while point D is Find the increase in flow between the reservoirs assuming the
on the upper level of the campus at an elevation of 66 m above same value of f for the two pipes. Also assume that the water levels
MSL. The source of supply is at 300 m from the junction at point in the reservoirs remain the same. (1mi = 5,280 ft or 1,610 m.)