Float valve for flow control

[mmaurigi]

I need to design a float that is attached to an arm that will open or close a butterfly valve that controls the level in a retention tank. It is identical the way the float works in a typical toilet. As the level decreases, the float moves down and opens the valve allowing more water in. As the water level rises, so does the float and that closes the valve. I've contacted the valve manufacturer and he said the shut-off torque for the valve is 850 in-lbs. I was figuring that the lever arm from the centerline of the valve shaft to the float would be about 36in. How do I calculate the size of the float so that will in fact float yet be able to provide the required torque to shut off the valve. If you can give me a hand with this I'd really appreciate it.

 

[abeltio]

This is a rough approach...
850in-lbs/36in = 23.6lbs
The volume of water that will give an upward force of 24lbs is 24lbs/[62.43 lb/cuft]= 0.384cuft
Design a sphere that will have a volume of 0.384cuft when submerged 1/6 of the diameter.
HTH
Saludos.
a.