HagenPoisseuille

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Liquid.Transport.HagenPoisseuille

Description

The component generates a volumetric flow rate due to a pressure difference between the ports for laminar flow in a cylindrical tube.

$\begin{equation*} \Delta p = 144 \, \frac{L \, \mu}{\pi \, d_{t}^{4}} \, q \end{equation*}$

Then the molar flow rates become

$\begin{equation*} F_{i} = q \, \left(c_{i}\right)_{upstream} \end{equation*}$

The energy flow rate is determined as

$\begin{equation*} \Phi = \sum_{i}^{N} F_{i} \, \left({\overline H}_{i}(T)\right)_{upstream} + F_{tot} \, \Big(H_{res}(T,p)\Big)_{upstream} \end{equation*}$

with

$\begin{equation*} F_{tot} = \sum_{i}^{N} F_{i} \end{equation*}$

The positive flow direction is from port A to port B.

Ports

Conserving

Liquid conserving port
```
Port_A = Liquid;  %
```
Liquid conserving port
```
Port_B = Liquid;  %
```

Output

Physical signal that represents the volumetric flow rate at upstream conditions
```
qout = {1,'l/s'};
```
Dependencies: The port is only visible when flowOutput is set to On.

Parameters

Options

Option to select flow output
```
flowOutput = OnOff.Off; 
```
On | Off

Geometry

Tube diameter
```
dt = {1,'cm'};
```
Tube length
```
delta  = {1.0e-03,'m'};
```

Nomenclature

$c_{i}$	concentration of species A_i
$F_{i}$	molar flow rate of species A_i
${\overline H}_{i}(T)$	molar enthalpy of species A_i
$\Delta H_{res}$	departure enthalpy of the mixture
$N$	total number of species
$q$	volumetric flow rate
$t$	time
$T$	temperature
$\Phi$	energy flow rate