\sqrt{\, z(t) \,} = \sqrt{\, H \, } - b \cdot t

b = \frac{\phi}{2} \cdot \frac{A}{S}  \cdot \sqrt{\, g \,}

\sqrt{\, p(t) \,} = \sqrt{\, p_0 \, } - b \cdot g \cdot t

p_0 = \rho \, g \, H

{\rm v}(t) = {\rm v}_0 - c \cdot g \cdot t

{\rm v}_0 = \phi \cdot \sqrt{2 \, g \, H}

c = \frac{\phi^2}{\sqrt{2}} \cdot \frac{A}{S}

q(t) = q_0 - d \cdot g \cdot t

q_0 = S \cdot \phi \cdot \sqrt{2 \, g \, H}

d = \frac{\phi^2}{\sqrt{2}} \cdot A

where

	fluid level in the tank above the tank bottom at time		initial fluid level in the tank above the tank bottom
	pressure at the bottom of the tank at time		initial pressure at the bottom of the tank
	outflow velocity at time		initial outflow velocity
	outflow rate at time		initial outflow rate
	cross-sectional area of the tank		cross-sectional area of the drainage orifice
	correction factor for the drainage orifice		gravity constant

See also