(1)	$\begin{array}{l}\displaystyle \dot m(t,l) = \dot m = \rm const\end{array}$

where

$\begin{array}{l}\dot m\end{array}$

mass flowrate along the pipe

The physical meaning of Pipe Flow Mass Conservation is that total mass passing through cross-section area of a pipe at any location of its trajectory is staying constant as there is no mass exchange of the fluid through the walls.

Equation (1) can be also written as:

(2)	$\begin{array}{l}\displaystyle \dot m(t,l) = \rho(p) \cdot q(t,l) = \rm const\end{array}$

where

$\begin{array}{l}\dot m\end{array}$	mass flowrate along the pipe
$\begin{array}{l}\rho(T, p)\end{array}$	fluid density
$\begin{array}{l}p(t,l)\end{array}$	fluid pressure distribution along the pipe
$\begin{array}{l}q(t,l)\end{array}$	volumetric flowrate of the pipe flow

Alternative forms

In case of a Pipe Flow with constant cross-section area $\begin{array}{l}A(l) = A = \rm const\end{array}$ it also leads to conservation of mass flux:

(3)	$\begin{array}{l}\displaystyle j_m(t,l) = j_m = \frac{\dot m}{A} = \rm const\end{array}$

where

$\begin{array}{l}j_m\end{array}$

mass flux along the pipe

Equation (3) can be also written as:

(4)	$\begin{array}{l}\displaystyle j_m = \rho \cdot u = \rm const\end{array}$

where

$\begin{array}{l}u\end{array}$

superficial velocity of the pipe flow

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Pipe Flow Mass Conservation

Alternative forms