Water flows along the horizontal pipe of cross section area 48 cm2 which has a c
ID: 2304974 • Letter: W
Question
Water flows along the horizontal pipe of cross section area 48 cm2 which has a constricti cross section area 12 cm2 at one place. If the speed of water at the constriction is 4 m/s, calculat wider section and hence the pressure at the constriction if the pressure in the wider sec 2. sp eed in the is 1.0 x 105 Pa. Density of water is 1000 kg/m tion [Ans. 1 m/s; 92.5 kPa] What volume of water will escape per minute from a tank through an opening 2 om in diameter and 3. 5 m below the level of the water? [Ans. 0.187 m*/min] uipped with a deferential mercury manometer as shown below. The inlet (section A venturi meter is eq 1) diameter is 30 cm and the throat (section 2) diameter is 15 cm. Find the ideal flow of water through the meter if the difference in height between the mercury columns is 23 cm. Relative density of mercury is 13.6 4. [Ans. 0.138 m3/min] 23 cm 5. Mercury at 20 °C is flowing in pipe of 50 mm diameter at a certain point A with velocity 1.83 m/s. the pipe travels to a point B, 3.78 above A, where the diameter has been reduced to 35 mm. The pipe continues to-a-point C, 1.27 m above B, at which the diameter has changed to 75 mm. The gauge pressure at A is 596 kPa. The relative density of mercury is 13.6, the atmospheric pressure is 101.325 kPa and the gravitational acceleration is 9.81 m/s. What would be the readings of the pressure gauges [Ans. 19 kPa; -60 kPa at points B and C? 6. A tank of large area is filled with water to a depth of 0.3 m. A hole of 5 cm2 cross section in the bottom allows water to drain out in a continuous stream. (a) What is the rate at which water flows out of the tank, in m3/s? (b) At what distance below the bottom of the tank is the cross-sectional area of the stream equal to one- [Ans. 1.22 x 103 m/s; 0.90 m] half the area of the hole? 7. Water in an enclosed tank is subjected to a gauge pressure of 6 x 105 Pa, applied by compressed air introduced into the top of the tank. A small hole, of 5 cm2 cross-sectional area, is in the side of the tank 5 m below the level of the water. Estimate the rate at which water escapes from this hole in m3/hr [Ans. 64.85 m3]Explanation / Answer
2. equation of continuity,
Q = A1 v1 = A2 v2
(48) (v1) = (12)(4)
v1 = 1 m/s .........Ans
Applying bernoulli's equation,
P1 + rho g h1 + rho v1^2 /2 = P2 + rho g h2 + rho v2^2 /2
(1 x 10^5) + 0 + (1000 x 1^2 / 2) = P2 + 0 + (1000 x 4^2 / 2)
P2 = 92.5 x 10^3 Pa Or 92.5 kPa
3. Applying bernoulli's equation,
P + rho g h + rho v^2 / 2 = constant
(101325) + (1000 x 9.8 x 5) + 0 = (101325) + (1000 v^2 / 2 )
v = sqrt(2 x 9.8x 5) = 9.90 m/s
A = pi d^2 / 4 = pi (0.02^2)/4 = (3.14 x 10^-4 ) m^2
Volume flow rate = Q = A v = 3.11 x 10^-3 m^3/s
Or (3.11 x 10^-3 m^3) / (1/60 min)
= 0.187 m^3 / min
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