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Thrust & Pressure

Mercury is po...

Question

Mercury is poured into a U-tube in which the cross-sectional area of the left-hand limb is three times.smaller than that of the right one. The level of the mercury in the narrow limb is a distance $l = 30 c m$ from the upper end of the tube. How much will the mercury level rise in the right-hand limb if the left one is filled to the top with water?

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Solution

PQ is original level of mercury. Equating the pressures at the level of M from left hand side and right hand side.
$P_{0} + ρ_{w} g h_{w} = P_{0} + ρ_{H g} g h_{H g}$
or $ρ_{w} h_{w} = ρ_{H g} h_{H g}$
$∴$ $(1) (30 + 3 x) = (13.6) (4 x)$
Solving we get,

$x = 0.58 c m$

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