A vessel of uniform cross-section open at the top with an orifice at its bottom contains oil (relative density 0.8 ) on top of water. It is immersed vertically in a large open tank of same oil as show

Question

A vessel of uniform cross-section open at the top with an orifice at its bottom contains oil (relative density 0.8 ) on top of water. It is immersed vertically in a large open tank of same oil as shown in figure. In which of following configuration will liquid level remain same. (Water does not come out or oil does not enter vessel) :- (Take : area of orifice $= 1 mm^{2}$ and area of vessel as $100 cm^{2}$ )

CT57 question 15 diagram

TestHub · Accepted Answer

No flow requires equal pressure at the orifice.
$ρ_{o} g h_{o} + ρ_{w} g h_{w} = 15 ρ_{o} g$
$ρ_{o} = 0.8 ρ_{w}$
Check each option in water-density units:
$A : 0.8 (5) + 8 = 12$
$B : 0.8 (12) + 2.4 = 12$
$C : 0.8 (8) + 4 = 10.4$
$D : 0.8 (12.5) + 2 = 12$
The outside pressure is 12 units. Answers: A, B, D.

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