First slide

Pressure in a fluid-mechanical properties of fluids

Question

When at rest, a liquid stands at the same level in the tubes as shown in the figure. But as indicated, a height difference h occurs when the system is given an acceleration a
towards the right. Then h is equal to

Moderate

A

$\frac{a L}{2 g}$
B

$\frac{g L}{2 a}$
C

$\frac{a L}{g}$
D

$\frac{g L}{a}$

Solution

Let P₁ and P₂ be the pressures at the bottom of the left and right ends of the tube, respectively.
$Then F = (P_{1} - P_{2}) A = ρ g h A$
where A is the cross section of the tube. The mass of the liquid in the horizontal portion is
$m = ρ L A$
$Now, F = m a$
$\Rightarrow ρ g h A = ρ L A a$
$\Rightarrow h = \frac{a L}{g}$

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