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Water flows into a large tank with flat bottom at the rate of 10^{-4}m^{3}s^{-1}. Water is also leaking out of a hole of area 1 cm^{2} at its bottom. If the height of the water in the tank remains steady, then this height is:

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

Answers (1)

best_answer

 

Torricelli's Theorem / Velocity of Efflux -

In fluid dynamics relating the speed of fluid flowing out of an orifice. 

- wherein

Given 

Q_{in}=10^{-4}\frac{m^{3}}{5}\\\\Ah=1cm^{2}=10^{2}\\h=const\\\\\Rightarrow Q_{in}=Q_{out}\\\\10^{-4}=AV_{out}-------(1)\\\\

If at point 1 velocity is zero  then velocity at point 2 which is at height h

h_{2}=h_{out}=\sqrt{2gh}----(2)put\: in\: eq^{n}(1)\\\10^{-4}=AV_{out}=10^{-4}\times \sqrt{2gh}\\\\\sqrt{2gh}=1\\\\2gh=1\\\\h=\frac{1}{2g}=\frac{1}{2\times 10}M\\\\h=5cm

 

 

 


Option 1)

Option 2)

Option 3)

Option 4)

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