6. A tank of large area is filled with water to a depth of 0.3 m. A hole of 5 cm

Question

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? (o) At what distance below the bottom of the tank is the cross-sectional area of the stream equal to one- half the area of the hole? [Ans. 1.22 x 103 m3/s; 0.90 m] Water in an enclosed tank is subiected 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 7. 5 m below the lev Ans. 64.85 m3]

Explanation / Answer

6. Applying bernoulli's equation,

P + rho g h + rho v^2 /2 = constant

P_atm + (1000 x 9.8 x 0.30) + 0 = P_atm + 0 + (1000 v^2 /2)

v = 2.426 m/s

and Q = A v = (5 x 10^-4 m^2)(2.425 m/s)

Q = 1.22 x 10^-3 m^3/s .......Ans

(B) Q = A1 v1 = A2 v2

A1 (2.426) = (A1/2) (v2)

v2 = 4.852 m/s

h = v2^2 / 2 g = (4.852^2) / (2 x 9.81)

h = 1.20 m

from bottom = 1.20 - 0.30 = 0.90 m

7. P1 + rho g h + rho v^2 /2 = constant

(P_atm + (6 x 10^5)) + (1000 x 9.8 x 5) + 0 = (P_atm) + 0 + (1000 v^2 / 2)

(6 x 10^5) + (49050) = 1000 v^2 /2

v = 36 m/s

Q = A v = (5 x 10^-4)(36) = 0.0180 m^3 /s

Q = (0.0180 m^3) /(1/3600 hr)

Q = 64.85 m^3 / hr

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