(ID 15713)

The definition of the volume flow ($J_V$) is the volume element ($\Delta V$) over the time elapsed ($\Delta t$):

which, in the limit of an infinitesimal time interval, corresponds to the derivative of the volume ($V$) with respect to the time ($t$):

(ID 15718)

The volume ($V$) for a tube with constant the section Tube ($S$) and a position ($s$) is

If the section Tube ($S$) is constant, the temporal derivative will be

$\displaystyle\frac{dV}{dt} = S\displaystyle\frac{ds}{dt}$

thus, with the volume flow ($J_V$) defined by

and with the flux density ($j_s$) associated with the position ($s$) via

it is concluded that

(ID 15717)

In the case that the flux density ($j_s$) is constant, the volume flow ($J_V$) can be calculated using the section or Area ($S$) according to:

If the flux density ($j_s$) varies, sufficiently small sectional elements $dS$ can be considered so that the equation remains valid in the sense that the contribution to flow is:

$dJ_V = j_s dS$

Integrating this expression over the entire section results in

(ID 15719)

(ID 15714)

The volume flow ($J_V$) corresponds to the quantity ERROR:9847,0 that flows through the channel during a time ($t$). Therefore, we have:

(ID 12713)

The volume ($V$) is calculated by multiplying the section Tube ($S$) with the position ($s$) along the tube:

(ID 4876)

The flux density ($j_s$) is related to the position ($s$), which is the fluid position at the time ($t$), through the following equation:

(ID 12714)

A flux density ($j_s$) can be expressed in terms of the volume flow ($J_V$) using the section or Area ($S$) through the following formula:

(ID 15716)

If the flux density ($j_s$) is not constant and varies across the flow tube section the volume flow ($J_V$), it is calculated as the integral over that section:

(ID 15712)