The figure below shows a leaky rain barrel filled with water with depth d = 1.20

Question

The figure below shows a leaky rain barrel filled with water with depth d = 1.20 m. Inside the barrel are two objects with equal size. Object A is made of wood and floats at the surface. Object B is made of gold and sits at the bottom. The density of water is 1000 kg m^-3. At a height h = 0.20 m, a small hole allows water to leak out of the barrel. The leak is so small that we can assume the water level in the barrel to be constant. Compare the buoyant force on object A with the buoyant force on object B. Are they the same, or, if not, which one is larger? Calculate the total pressure in the water at the level of the hole. Assuming laminar flow, and that pressure just outside the hole is the atmospheric pressure, calculate the horizontal speed of the water flow just outside the hole.

Explanation / Answer

buoyant force on object = volume of object immersed*density of fluid *g

so buoyany force on gold object is more because it has higher volume immersed

(b) pressure at hole level=101325 +(density of water*g*(1.2-0.2))=111125 pa

(c) by bernauli theorem

pressure difference=0.5*density of water*velocity^2=9800

velocity=4.43 m/s

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