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A small hole of area of cross-section 2 ...

A small hole of area of cross-section 2 `mm^(2)` present near the bottom of a fully filled open tank of height 2. Taking g=`10m//s^(2)`, the rate of flow of water through the open hole would be nearly

A

`12.6 xx 10^(-6) m^(3)//s`

B

`8.9 xx 10^(-6)m^(3)//s`

C

`2.23 xx 10^(-6)m^(3)//s`

D

`6.4 xx 10^(-6) m^(3)//s`

Text Solution

Verified by Experts

The correct Answer is:
A

Rate the flow liquid Q= A u = `A sqrt(2gh)`
`=2 xx 10^(-6) m^(2) xx sqrt(2 xx 10 xx 2)m//s`
`=2 xx 2 xx 3.16 xx 10^(-6) m^(3)//s`
`=12.64 xx 10^(-6) m^(3)//s`
`=12.6 xx 10^(-4) m^(3)//s`
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Knowledge Check

  • The level of water in a tank is 5 m high. A hole of area of cross section 1 cm^(2) is made at the bottom of the tank. The rate of leakage of water for the hole in m^(3)s^(-1) is (g=10ms^(-2))

    A
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    C
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    D
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  • A cylindrical vessel open at the top is 20cm high and 10 cm in diameter. A circular hole of cross-sectional area 1cm^(2) is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of 10^(2)cm^(3)//s . The height of water in the vessel under steady state is (Take g=10m//s^(2)) .

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