Page 197 - Water Engineering Hydraulics, Distribution and Treatment

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(0.0736 m ). The cross-sectional area A of the lower part is 0.5 ft
D
U
2
Upper pipe
(0.0464 m ). The height of the upper part a = 5 ft (1.524 m), the
height of the lower part b = 5 ft (1.524 m) and the water surface
area A of the upper part is 20 ft (1.8581 m ). Determine the force
W
R
B
tending to push the plug out.
h
(1)
D
L
5.19
Determine the components of the forces P and P due to the
Lower pipe
water acting on the curved area AB in Fig. 5.39 per unit length ft (m).
Datum
Also locate the components of these forces P and P The radius
r is 6.5 ft (1.98 m). The center of gravity of a quadrant of a circle
E
A
is located at a distance 4r∕3 from either mutually perpendicular
radius.
Water surface A 2 C 2 x x O y. y 2 Figure 5.40 Pipe line analysis. (2) Problems/Questions 175
5.24
In the sketch shown in Fig. 5.41 a barrel whose empty weight
Hinge
is 60 lb (27.2 kg) contains an unknown quantity of water in which
r a container holding 200 lb (90.8 kg) of oil (specific gravity = 0.95)
y floats, and a beaker containing 10 lb (4.54 kg) of mercury (specific
gravity = 13.00) floats in the oil. The beaker, the oil container, and
the barrel are 6, 24, and 36 in. (0.1524, 0.6096, and 0.9144 m)
P x in diameter, respectively. The total weight indicated by the scale is
x
860 lb (390.44 kg). Determine the height h of the water in the barrel.
B
Hg
P y h
Oil
Figure 5.39 Hydrostatic force analysis.
Water
5.20 Determine (1) the total resultant force acting on an inclined
rectangular gate shown in Fig. 5.7, and (2) the location of the
pressure center. Assume a = 5 ft (1.52 m), b = 6 ft (1.83 m),
◦
h = 4 ft (1.22 m), and = 60 .
5.21 An object is 1.5 ft (0.4572 m) wide by 2.5 ft (0.762 m) long Figure 5.41 Water barrel, oil container, and mercury beaker.
and 1.5 ft (0.4572 m) high. It weighs 150 lb (68.1 kg) at a water
depth of 10 ft (3.048 m). What is the weight of the object in air and 5.25 Determine the force in lb (N) that each connection between
what is its specific gravity? ◦
the 90 elbow and the 12-in. (0.3048-m)-diameter pipe line in
Fig. 5.42 will resist. Assume the water in the system is static (no
5.22 A prismatic object is 8 in. (20.32 cm) thick, 8 in. (20.32 cm) flow condition) and the pipeline is pressured to 100 psig (694 kPa
wide, and 16 in. (40.64 cm) long. It weighs 12 lb (5.45 kg) at a gauge).
water depth of 20 in. (50.8 cm). What is the weight of the object in
air and what is its specific gravity? D
A
5.23 A horizontal pipe carrying oil of specific gravity 0.8 is 6 in.
B
(15.24 cm) in diameter. Near the end E, the pressure is measured
to be 13.2 psi (91.6 kPa). After E, the 6 in. (15.24 cm) pipe turns
◦
◦
90 upwards for 12 ft (3.66 m) reaching another 90 bend, which
connects to an upper horizontal pipe having a diameter of 18 in.
(45.72 cm) at point R where the pressure is also measured to be
Figure 5.42 Elbow connecting two pipes.
8.75 psi (60.73 kPa) (Fig. 5.40). Determine
1. The oil velocities in the two horizontal pipes
5.26 A conical reducing section shown in Fig. 5.43 connects an
2. The direction of oil flow existing 6 in. (152.4 mm) pipeline with a new 4-in. (101.6-mm)-
3
3. The head loss between E and R, if the oil discharge is 5 ft /s diameter pipeline. Assume the pipeline is at 100 psig (694 kPa =
3
2
(0.1415 m /s) 694 kN/m ) static pressure under no flow conditions and there is no