3. A cylindrical tank contains water up to a level of 10m. The base of the tank

Question

3. A cylindrical tank contains water up to a level of 10m. The base of the tank has a diameter of 4m. At a height of ½ meter from the bottom there is an escape of diameter of 5cm. Calculate: (A) The force exerted by the fluid at the bottom of the tank, (B) The rapid escape of the fluid, (C) The rate at which the fluid level drops. 3. A cylindrical tank contains water up to a level of 10m. The base of the tank has a diameter of 4m. At a height of ½ meter from the bottom there is an escape of diameter of 5cm. Calculate: (A) The force exerted by the fluid at the bottom of the tank, (B) The rapid escape of the fluid, (C) The rate at which the fluid level drops. 3. A cylindrical tank contains water up to a level of 10m. The base of the tank has a diameter of 4m. At a height of ½ meter from the bottom there is an escape of diameter of 5cm. Calculate: (A) The force exerted by the fluid at the bottom of the tank, (B) The rapid escape of the fluid, (C) The rate at which the fluid level drops.

Explanation / Answer

The pressure exerted at the bottom of the tank is

Given data: height h = 10m, density of water d = 1000Kg/m3, acceleration due to gravity g = 9.8 m/s2

As the volume of the tank is constant, substituting the respective quantities we get

a) Force at the bottom of the tank = (10)(1000)(9.8) = 98kN

b) The escape is at a height of 0.5m from the bottom. Therefore, the depth of the escape is 10-0.5 = 9.5m

The velocity of escape of water is

that is

= 13.65m/s

c) Rate of flow = Av

A is the flow area and v is the velocity of flow

   = 0.002m2

Flow rate = 0.002 * 13.65 = 0.0267 m3/s

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