First slide

Fluid statics

Question

A sealed tank containing a liquid of density ρ moves with a horizontal acceleration a, as shown in the figure. The difference in pressure between the points A and B is

Moderate

A

hρg
B

lρa
C

hρg - lρa
D

hρg + lρa

Solution

Consider narrow tubes AB and BC each of cross-sectional area ΔS.
In Fig-(1): p_B.ΔS - p_A.ΔS = (ρ.ΔS.l).a ⇒ p_B - p_A= ρal.....(1)
In Fig-(2): p_B.ΔS + (ρ.ΔS.h)g = p_C.ΔS ⇒ p_C - p_B= ρgh.....(2)
Adding, p_C - p_A = (ρal + ρgh)

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