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Flow controller moment balance Flow controller moment balance

flow controller moment balance

where

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{latex}$\Delta h_{flow controller}${latex}

is the change in depth of the liquid level in the constant head tank and

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{latex}$A_{float}${latex}

is the cross sectional area of the cylindrical float. Thus

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{latex}$\Delta h_{flow controller} A_{float}${latex}

is the submerged volume of the float that when multiplied by the density,

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{latex}$\rho${latex}

and by acceleration due to gravity is equal to the total buoyant force acting on the float. The lever arm for the float has a length

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{latex}$L_{float\;lever\;arm}${latex}

. The moment acting to open the valve is provided by the pressure of liquid from the stock tank,

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{latex}$\rho g\Delta h_{stock}${latex}

, acting over the area of the valve opening

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{latex}$A_{orifice}${latex}

. The lever arm for the opening moment is

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{latex}$L_{valve\;lever\;arm}${latex}

.

The float valve attenuation can be obtained by rearranged the previous equation and solving for the ratio of the change in height of the stock tank divided by the change in height of the constant head tank.

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