mechanisms

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

equation=4347

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

equation=12713

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

equation=4876

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

equation=12713

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

equation=12714

it is concluded that

equation=15716

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:

equation=15716

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

equation=15712

model

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

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

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

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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:

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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:

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