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A liquid of density \rho is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be:

 

  • Option 1)

     

    \frac{3}{4}\rho v^{2}

  • Option 2)

     

    \frac{1}{4}\rho v^{2}

  • Option 3)

     

    \rho v^{2}

  • Option 4)

     

    \frac{1}{2}\rho v^{2}

Answers (1)

best_answer

 

Torricelli's Theorem / Velocity of Efflux -

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

- wherein

Momentum per second carried by liquid per second 

\varrho aV^{2}

Net force 

1. due to reflected liquid = 2[\frac{1}{4}\varrho aV^{2}]

2. due to stopped liquid = \frac{1}{4}\varrho aV^{2}

Total force = \frac{3}{4}\varrho aV^{2}

\because P=\frac{3}{4}\varrho aV^{2}

 

 


Option 1)

 

\frac{3}{4}\rho v^{2}

Option 2)

 

\frac{1}{4}\rho v^{2}

Option 3)

 

\rho v^{2}

Option 4)

 

\frac{1}{2}\rho v^{2}

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