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Question

A very small hole is made at the bottom of a tank filled with water (density =1000 kg/m3). If the total pressure at the bottom of the tank is 3 atm (1 atm=105 N/m2), then the velocity of efflux is:
Take g=10 m/s2.

A
20 m/s
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B
300 m/s
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C
600 m/s
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D
500 m/s
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Solution

The correct option is A 20 m/s
Pressure at hole, P2=3 atm
Pressure at open end of tank is P1=1 atm
Since the hole is also open to atmosphere, excess pressure P2P1=2 atm at the hole is due to hydrostatic pressure of water column above the hole.
ρgh=P2P1=2 atm
Or, ρgh=2×105 N/m2
h=2×105103×10=20 m
Cross-sectional area of tank is very large compared to area of the hole (very small), i.e A1>>A2
Hence, we can apply formula for velocity of efflux at the bottom of the tank:
v=2gh
Or, v=2×10×20
v=20 m/s

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