The ball opearted valve show in the figure below control the flow from a tank th

Question

The ball opearted valve show in the figure below control the flow from a tank through a pipe to a lower tank in which it is situated. The water level in he upper tank is 7m above the 10mm diameter valve opening. Calculate the volume of the ball which must be submerged to keep the valve closed.

Explanation / Answer

The force exerted by the water in the water tank to the valve=The force exerted by the moment produced by the submerged ball Force due to water=pho*volume*g=1*(2*pi*radius*7)*9.8;r=0.005 If volume of ball that was submerged is V the force exerted by water on the ball is 1*V*9.8 then force exerted on the valve due to lever is 5*1*V*9.8 =====>5*V*9.8=2*pi*0.005*7*9.8 =====>V=0.043 m^3 (This is theVOLUME SUBMERGED) to obtain volume of the ball YOU MUST PROVIDE DENSITY OF BALL If density was pho then weight of ball=byouancy force pho*V_ac=V Volume of ball=0.043/pho m^3

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