A common type of liquid level control in tanks and reactors is the float level c

Question

A common type of liquid level control in tanks and reactors is the float level control valve. An example is shown below. If this looks familiar is because you have seen one of these in your toilet bowl! The control is very simple: a float is connected to a valve, that closes due to the buoyancy force of the float as the correct liquid level is achieved. The force created is solely from the floats buoyancy (thus, this is an entirely mechanical control). The unit is designed so that the force required to close the valve is half of the net buoyance force to ensure the correct force is achieved and the valve closes. Calculate the volume of the float valve required (in Liters) if the unit will be used in ethanol at 25°C and the force required to close the valve is 10 N. The mass of the float (plus the extension tube that holds the float) is 100 g. (6 pts)

Explanation / Answer

as per the data provided in the question we have one equation to solve the given problem

Fforce = (1/2)*Fbouyancy

Fbouyancy is nothing but the buoyancy force and Fforce is the force required o close the valve

Now,

Fforce = 10 N

buoyancy force is given by

F =Density of fluid * Volume of object * g

Now at T = 25 oC, Density of fluid, i.e, ethanol in our case is 789 Kg/m3

Hence we can write the equation

10 = (1/2)*789*V*g

10 = (1/2)*789*V*9.81

V = 0.00258 m3 = 2.5839 Liters

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