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Question

A larger tank with a nozzle attached contains three immiscible fluids as shown in figure. Assuming that the changes in h1,h2 and h3 are negligible, the discharge velocity at this instant is


A
2gh3(1+ρ1ρ3h1h3+ρ1ρ3h2h3)
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B
2g(h1+h2+h3)
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C
2g(ρ1h1+ρ2h2+ρ3h3ρ1+ρ2+ρ3)
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D
 2g(ρ3h2h3+ρ2h3h1+ρ1h2h31h1+2h2+3h3)
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Solution

The correct option is A 2gh3(1+ρ1ρ3h1h3+ρ1ρ3h2h3)
Gauge pressure at point A is
PA=ρ1gh1+ρ2gh2+ρ3gh3(i)
Gauge Pressure at point B is
PB=0
Applying Bernoulli's equation between point A and B.
PA+(ρgh)A+12ρv2A=PB+(ρgh)B+12ρv2B
[PB=0 & (ρgh)A=(ρgh)B at same height; vA=0]
PA=12ρ3v2B [ρ=ρ3 at point B]
ρ1gh1+ρ2gh2+ρ3gh3=12ρ3v2B
[using (i)]
vB=2gρ3(ρ1h1+ρ2h2+ρ3h3)
=2gh3(ρ1h1ρ3h3+ρ2h2ρ3h3+1)
vB=2gh3(1+ρ1h1ρ3h3+ρ2h2ρ3h3)

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