First slide

Fluid dynamics

Question

There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to

Easy

Solution

By Toriceli's equation, $\large V_1=\sqrt {2gh_1}$ and $\large V_2=\sqrt {2gh_2}=\sqrt {2g(h_1+h)}$
p₁ = Rate of flow of momentum of water through orifice 1 = ρ.a.V₁² = 2ρagh₁
p₂ = Rate of flow of momentum of water through orifice 2 = ρ.a.V₂² = 2ρag(h₁+h)
$\large \therefore$ Resultant force exerted by water on the vessel = (p₂ - p₁) = 2ρagh. Here 'a' = area of each hole and ρ = density of water. Hence option (2) is right.

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