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  • A cylindrical container of radius ' R ' and height ' h ' is completely filled with  liquid.&nb

A cylindrical container of radius ' R ' and height ' h ' is completely filled with  liquid.  Two horizontal L shaped pipes of small cross-section area ' a ' are connected to the cylinder as shown in the figure. Now the two pipes are opened and fluid starts coming out of the pipes horizontally in opposite directions. Then the torque due to ejected liquid on the system is:        

                            

Option: 1

4\; a\: g\: h_{P}R       


Option: 2

8\; a\: g\: h_{P}R    


Option: 3

2\; a\: g\: h_{P}R


Option: 4

 none of these


Answers (1)

best_answer

 

Torricelli's Theorem / Velocity of Efflux -

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

- wherein

 

 

Velocity of efflux of water \left ( V \right )=\sqrt{2g\left [ \frac{h}{2}\right ]}=\sqrt{gh}

force on ejected water = Rate of change of momentum of ejected water.        

=\rho \left ( av \right )\left ( v \right )\; \; \; =\rho\; av^{2}

Torque of these forces about central line   

=\left ( \rho av^{2} \right )2R\; .\; 2\; =4\rho av^{2}R=4\rho \; agh\; R

 

Posted by

Ajit Kumar Dubey

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