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Consider an open cylindrical barrel of diameter 0.5 m. Installed in the bottom o

ID: 1900143 • Letter: C

Question

Consider an open cylindrical barrel of diameter 0.5 m. Installed in the bottom of the barrel is a pipe (10 cm in diameter) which permits liquid to flow out under gravity. At the same time, liquid is added to the tank from above through a pipe with a diameter of 5 cm.
a. If the velocity of the liquid leaving through the bottom pipe is 2.21 m/s, what is the velocity of the liquid entering the tank (from pipe above) if the level of the liquid in the tank is constant? ans. 8.81 m/s
b. If the velocity of the liquid leaving through the bottom pipe is 2.21 m/s and at that instant it is observed that the level in the tank is increasing at the rate of 1 cm/s, what is the velocity of the liquid entering the tank from the inlet pipe? ans. 9.81 m/s

Explanation / Answer

a)

A1 v1 = A2 v2

R1^2 v1 = R2^2 v2

10^2 * 2.21 = 5^2 v2^2

v2 = 8.84 m/s

b)

A1 v1 + A3 v3 = A2 v2

R1^2 v1 + R3^2 v3= R2^2 v2

10^2 * 2.21 + 50^2 * 0.01 = 5^2 v2^2

v = 9.84 m/s