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Time to Empty Tank Formula and Calculator

Time to Empty Tank through Orifice Formula and Calculator

Drainage time for constant cross section, no inflow

${\displaystyle t=\frac{2A_r}{c{A}_o\sqrt{2g}}(h_1^{1/2}-<!--\; -\; -->h_2^{1/2})}$

Inflow < outflow, constant cross section

${\displaystyle t={\int <!--\; \int \; -->}_{h_1}^{h_2}\frac{-<!--\; -\; -->A_{T}dh}{Q_{out}-<!--\; -\; -->Q_{in}}}$

Vertical Tank

where
A_T = surface area of fluid, ft², (m²)
g = gravity, ft/s² ( m/s²)
c = constant
A_o = orifice area, ft², (m²)
h_{1 & 2 =} Fluid level above the orifice range (from - to), ft, m
Q_{out & in} = flow in, ft/s³ ( m/s³)

Source:

Schaum's Outline of Fluid Mechanics and Hydraulics

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