Question:
A wide vessel with a hole in the bottom is filled with water and kerosene ....neglecting viscocity find velocity of water flow if the thickness of water layer is 30cm and thickness of kerosene layer is 20cm
Answer:
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Consider a wide vessel with a hole in the bottom as shown in the diagram. As the density of the water is greater than the density of the kerosene, it will collect at the bottom.
Let the height of water and kerosene be h1 and h2 respectively and their corresponding densities be ρ1 and ρ2
The pressure due to water and kerosene level together would be h1 ρ1 g + h2 ρ2 g
As the water flows from the hole at the bottom of the vessel, there is a kinetic energy involved which is ½ ρ1 v2
Hence, h1 ρ1 g + h2 ρ2 g = ½ ρ1 v2
Divide throughout by ρ1 , we get h1 g + h2 (ρ2 / ρ1) g = ½ v2
Hence, v = [ 2 (h1 + h2 (ρ2 / ρ1) ) g ]1/2
Substituting the values of h1 = 30 * 10-2 m, h2 = 20 * 10-2 m, (ρ2 / ρ1)= 0.80
V = (9.016)1/2 = approximately 3 m/s
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