fluid_mechanics
82 Chapter 2 ■ Fluid Statics Vapor 1 m Open Ocean surface 1 m 1 m Liquid h 735 mm Seawater 360 mm Shell wall 10 m Mercury Mercury Shell F I G U R E P2.35 2.36 Determine the elevation difference, ¢h, between the water levels in the two open tanks shown in Fig. P2.36. SG = 0.90 0.4 m Δh F I G U R E P2.38 *2.39 Both ends of the U-tube mercury manometer of Fig. P2.39 are initially open to the atmosphere and under standard atmospheric pressure. When the valve at the top of the right leg is open, the level of mercury below the valve is h i . After the valve is closed, air pressure is applied to the left leg. Determine the relationship between the differential reading on the manometer and the applied gage pressure, p g . Show on a plot how the differential reading varies with p g for h i 25, 50, 75, and 100 mm over the range 0 p g 300 kPa. Assume that the temperature of the trapped air remains constant. 1 m p g Valve Water F I G U R E P2.36 h i 2.37 For the configuration shown in Fig. P2.37 what must be the value of the specific weight of the unknown fluid? Express your answer in lb/ft 3 . Mercury F I G U R E P2.39 Open Water Open 2.40 The inverted U-tube manometer of Fig. P2.40 contains oil 1SG 0.92 and water as shown. The pressure differential between pipes A and B, p A p B , is 5 kPa. Determine the differential reading, h. 5.5 in. 4.9 in. Oil 1.4 in. Unknown fluid 3.3 in. 0.2 m h A F I G U R E P2.37 Water 0.3 m 2.38 An air-filled, hemispherical shell is attached to the ocean floor at a depth of 10 m as shown in Fig. P2.38. A mercury barometer located inside the shell reads 765 mm Hg, and a mercury U-tube manometer designed to give the outside water pressure indicates a differential reading of 735 mm Hg as illustrated. Based on these data what is the atmospheric pressure at the ocean surface? F I G U R E P2.40 B 2.41 An inverted U-tube manometer containing oil (SG 0.8) is located between two reservoirs as shown in Fig. P2.41. The
Problems 83 8 psi Carbon tetrachloride A B 0.7 ft Oil Brine 3 ft 1 ft Water h Brine 12 in. 1 ft Carbon tetrachloride F I G U R E P2.41 θ reservoir on the left, which contains carbon tetrachloride, is closed and pressurized to 8 psi. The reservoir on the right contains water and is open to the atmosphere. With the given data, determine the depth of water, h, in the right reservoir. 2.42 Determine the pressure of the water in pipe A shown in Fig. P2.42 if the gage pressure of the air in the tank is 2 psi. Air p = 2 psi 1 ft 4 ft 2 ft Water F I G U R E P2.42 SG = 0.9 2.43 In Fig. P2.43 pipe A contains gasoline 1SG 0.72, pipe B contains oil 1SG 0.92, and the manometer fluid is mercury. Determine the new differential reading if the pressure in pipe A is decreased 25 kPa, and the pressure in pipe B remains constant. The initial differential reading is 0.30 m as shown. A F I G U R E P2.44 2.45 Determine the new differential reading along the inclined leg of the mercury manometer of Fig. P2.45, if the pressure in pipe A is decreased 10 kPa and the pressure in pipe B remains unchanged. The fluid in A has a specific gravity of 0.9 and the fluid in B is water. A SG = 0.9 30° 100 mm 50 mm F I G U R E P2.45 Water Mercury 2.46 Determine the change in the elevation of the mercury in the left leg of the manometer of Fig. P2.46 as a result of an increase in pressure of 5 psi in pipe A while the pressure in pipe B remains constant. A Water 18 in. 6 in. Oil (SG = 0.9) B B 80 mm 12 in. A 0.4 m Oil B 30° 1_ in. 2 diameter Mercury F I G U R E P2.46 1_ in. diameter 4 Gasoline 0.3 m Mercury 2.47 The U-shaped tube shown in Fig. P2.47 initially contains water only. A second liquid with specific weight, g, less than water is placed on top of the water with no mixing occurring. Can the F I G U R E P2.43 2.44 The inclined differential manometer of Fig. P2.44 contains carbon tetrachloride. Initially the pressure differential between pipes A and B, which contain a brine 1SG 1.12, is zero as illustrated in the figure. It is desired that the manometer give a differential reading of 12 in. (measured along the inclined tube) for a pressure differential of 0.1 psi. Determine the required angle of inclination, u. γ h D 1 = 1.5 D 2 D 2 Water F I G U R E P2.47
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82 Chapter 2 ■ Fluid Statics<br />
Vapor<br />
1 m<br />
Open<br />
Ocean surface<br />
1 m<br />
1 m<br />
Liquid<br />
h<br />
735 mm<br />
Seawater<br />
360 mm<br />
Shell wall<br />
10 m<br />
Mercury<br />
Mercury<br />
Shell<br />
F I G U R E P2.35<br />
2.36 Determine the elevation difference, ¢h, between the water<br />
levels in the two open tanks shown in Fig. P2.36.<br />
SG = 0.90<br />
0.4 m<br />
Δh<br />
F I G U R E P2.38<br />
*2.39 Both ends of the U-tube mercury manometer of Fig. P2.39<br />
are initially open to the atmosphere and under standard atmospheric<br />
pressure. When the valve at the top of the right leg is open, the level<br />
of mercury below the valve is h i . After the valve is closed, air pressure<br />
is applied to the left leg. Determine the relationship between the<br />
differential reading on the manometer and the applied gage pressure,<br />
p g . Show on a plot how the differential reading varies with p g for<br />
h i 25, 50, 75, and 100 mm over the range 0 p g 300 kPa.<br />
Assume that the temperature of the trapped air remains constant.<br />
1 m<br />
p g<br />
Valve<br />
Water<br />
F I G U R E P2.36<br />
h i<br />
2.37 For the configuration shown in Fig. P2.37 what must be the<br />
value of the specific weight of the unknown <strong>fluid</strong>? Express your<br />
answer in lb/ft 3 .<br />
Mercury<br />
F I G U R E P2.39<br />
Open<br />
Water<br />
Open<br />
2.40 The inverted U-tube manometer of Fig. P2.40 contains oil<br />
1SG 0.92 and water as shown. The pressure differential between<br />
pipes A and B, p A p B , is 5 kPa. Determine the differential<br />
reading, h.<br />
5.5 in.<br />
4.9 in.<br />
Oil<br />
1.4 in.<br />
Unknown<br />
<strong>fluid</strong><br />
3.3 in.<br />
0.2 m<br />
h<br />
A<br />
F I G U R E P2.37<br />
Water<br />
0.3 m<br />
2.38 An air-filled, hemispherical shell is attached to the ocean<br />
floor at a depth of 10 m as shown in Fig. P2.38. A mercury<br />
barometer located inside the shell reads 765 mm Hg, and a<br />
mercury U-tube manometer designed to give the outside water<br />
pressure indicates a differential reading of 735 mm Hg as<br />
illustrated. Based on these data what is the atmospheric pressure<br />
at the ocean surface?<br />
F I G U R E P2.40<br />
B<br />
2.41 An inverted U-tube manometer containing oil (SG 0.8) is<br />
located between two reservoirs as shown in Fig. P2.41. The