(1)	$\begin{array}{l}\displaystyle \sqrt{\, z(t) \,} = \sqrt{\, H \, } - b \cdot t\end{array}$

(2)	$\begin{array}{l}\displaystyle b = \frac{\phi}{2} \cdot \frac{A}{S} \cdot \sqrt{\, g \,}\end{array}$

(3)	$\begin{array}{l}\displaystyle \sqrt{\, p(t) \,} = \sqrt{\, p_0 \, } - b \cdot g \cdot t\end{array}$

(4)	$\begin{array}{l}\displaystyle p_0 = \rho \, g \, H\end{array}$

(5)	$\begin{array}{l}\displaystyle {\rm v}(t) = {\rm v}_0 - c \cdot g \cdot t\end{array}$

(6)	$\begin{array}{l}\displaystyle {\rm v}_0 = \phi \cdot \sqrt{2 \, g \, H}\end{array}$

(7)	$\begin{array}{l}\displaystyle c = \frac{\phi^2}{\sqrt{2}} \cdot \frac{A}{S}\end{array}$

(8)	$\begin{array}{l}\displaystyle q(t) = q_0 - d \cdot g \cdot t\end{array}$

(9)	$\begin{array}{l}\displaystyle q_0 = S \cdot \phi \cdot \sqrt{2 \, g \, H}\end{array}$

(10)	$\begin{array}{l}\displaystyle d = \frac{\phi^2}{\sqrt{2}} \cdot A\end{array}$

where

$\begin{array}{l}z(t)\end{array}$	fluid level in the tank above the tank bottom at time $\begin{array}{l}t\end{array}$	$\begin{array}{l}H = z(0)\end{array}$	initial fluid level in the tank above the tank bottom
$\begin{array}{l}p(t)\end{array}$	pressure at the bottom of the tank at time $\begin{array}{l}t\end{array}$	$\begin{array}{l}p_0 = p(0)\end{array}$	initial pressure at the bottom of the tank
$\begin{array}{l}{\rm v}(t)\end{array}$	outflow velocity at time $\begin{array}{l}t\end{array}$	$\begin{array}{l}{\rm v}_0 = {\rm v}(0)\end{array}$	initial outflow velocity
$\begin{array}{l}q(t)\end{array}$	outflow rate at time $\begin{array}{l}t\end{array}$	$\begin{array}{l}q_0 = q(0)\end{array}$	initial outflow rate
$\begin{array}{l}A\end{array}$	cross-sectional area of the tank	$\begin{array}{l}S\end{array}$	cross-sectional area of the drainage orifice
$\begin{array}{l}\phi\end{array}$	correction factor for the drainage orifice	$\begin{array}{l}g\end{array}$	gravity constant

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See also