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Question

Equal volumes of two immiscible liquids of densities ρ and 2ρ are filled in a vessel as shown figure. Two small holes are punches at depth h/2 and 3h/2 from the surface of lighter liquid. If v1 and v2 are the velocities of a flux at these two holes then v1/v2 is :

126058_d0b68670265d4eea99f911c0b1594f4d.png

A
122
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B
12
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C
14
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D
12
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Solution

The correct option is D 12

Here, two small holes are punches at depth h2 and 3h2 from the surface of lighter liquid. Hence, the height of first hole from the surface of lighter liquid is
h1=h2
and the height of second hole from the first hole is(i.e. from surface of remaining liquid)
h2=3h2h2=h
Now, we have the velocity of flux from first hole is
v1=2h1g
v1=2(h2)g
v1=hg
Applying Bernoulli's equation to point just inside and outside the second hole,
Pa+ρgh+2ρgh2=Pa+122ρv2
v=2gh
So, the velocity of flux from second hole is
v2=2hg
Therefore,
v1v2=hg2hg
v1v2=12

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