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Question

As shown in figure a liquid of density ρ is standing in a sealed container to a height h. The container contains compressed air at gauge pressure of p. The horizontal outlet pipe at E has a cross sectional area half of that at C. After the outlet is open, choose the correct option(s)


A
The velocity of liquid at C will be ((p+ρgh)2ρ]12
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B
The velocity of liquid at C will be (2(p+ρgh)ρ]12
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C
h1=3V2C2g, where VC is the velocity at point C
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D
pC>pE, where pC and pE  are pressures at point C and E
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Solution

The correct options are
A The velocity of liquid at C will be ((p+ρgh)2ρ]12
C h1=3V2C2g, where VC is the velocity at point C
D pC>pE, where pC and pE  are pressures at point C and E
pA=p+po+ρgh .................(i)
Apply Bernoulli's theorem at A, C and E
(p+po)+ρgh=pC+ρV2C2=po+ρV2E2 ...................(ii) pC=po+ρgh1 ..................(iii) ACVC=AEVE   ACVC=(AC2)VE ......................(iv)  From eq. (i), (po+ρgh1)+ρV2C2=po+ρ(2VC)22 ρgh1=2ρV2Cρ2V2C=32ρV2C or  h1=3V2C2g From eq. (ii), (p+po)+ρgh=(po+ρgh1)+ρV2C2 p+ρgh=ρg(3V2C2g)+ρV2C2 V2C=(p+ρgh)2ρ 

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