First slide

Fluid dynamics

Question

A liquid is poured into a vessel at rest with the hole in the wall closed. It is filled to a height H. With what horizontal acceleration should the vessel be moved so that the liquid does not come out, when the hole is opened ?

Difficult

A

g
B

, $2 g (H / l)$
C

$2 g (h / l)$
D

$2 g (H - h) / l$

Solution

If A be the area of the hole and p, the density of the liquid, then
$F = \frac{ΔP}{Δt} = \frac{Δ (mv)}{Δt} = \frac{VΔm}{Δt} = \frac{VΔ (Vρ)}{Δt} = vρ (\frac{ΔV}{Δt}) = vρ [volurne flowing / \sec] = vρ [Av] = v^{2} Aρ v = Velocity of liquid coming out ftom hole, i.e., V = \sqrt{(2 gh)} ∴ F = (2 gh) Aρ The mass of the liquid on which this force acts m = Alρ Now a = \frac{F}{m} = \frac{(2 gh) Aρ}{Alρ} = \frac{2 gh}{l}$

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