(1)	$\begin{array}{l}\displaystyle < A>_t \, = \frac{1 }{Q(t)} \int_{t_0}^t A(t) \ q(t) \, dt\end{array}$

where

$\begin{array}{l}t\end{array}$	time-line
$\begin{array}{l}t_0\end{array}$	initial time
$\begin{array}{l}A(t)\end{array}$	time-based variable
$\begin{array}{l}q(t)\end{array}$	volumetric flowrate
$\begin{array}{l}Q(t)\end{array}$	cumulative flow $\begin{array}{l}Q(t) = \int_{t_0}^t q(t) \, dt\end{array}$

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See also