General resistance in a moist air branch

**Library:**Simscape / Foundation Library / Moist Air / Elements

The Flow Resistance (MA) block models a general
pressure drop in a moist air network branch. The drop in pressure is proportional to the
square of the mixture mass flow rate and inversely proportional to the mixture density.
The constant of proportionality is determined from a nominal operating condition
specified in the block dialog box. Set the **Nominal mixture density**
parameter to zero to omit the density dependence.

Use this block when empirical data on the pressure losses and flow rates through a component is available, but detailed geometry information is unavailable.

The block equations use these symbols.

$$\dot{m}$$ | Mass flow rate |

Φ | Energy flow rate |

p | Pressure |

ρ | Density |

R | Specific gas constant |

S | Cross-sectional area |

K | Proportionality constant |

h | Specific enthalpy |

T | Temperature |

Subscripts `a`

, `w`

, and `g`

indicate the properties of dry air, water vapor, and trace gas, respectively. Subscripts
`A`

and `B`

indicate the appropriate port.

Mass balance:

$$\begin{array}{l}{\dot{m}}_{A}+{\dot{m}}_{B}=0\\ {\dot{m}}_{wA}+{\dot{m}}_{wB}=0\\ {\dot{m}}_{gA}+{\dot{m}}_{gB}=0\end{array}$$

Energy balance:

$${\Phi}_{A}+{\Phi}_{B}=0$$

If the **Nominal mixture density** parameter value,
*ρ*_{nom}, is greater than zero, then the block
computes the pressure drop as

$${p}_{A}-{p}_{B}={K}_{1}{\dot{m}}_{A}\sqrt{{\dot{m}}_{A}^{2}+{\left({f}_{lam}{\dot{m}}_{nom}\right)}^{2}}\frac{R{T}_{in}}{{p}_{in}}$$

where:

*f*_{lam}is the fraction of nominal mixture mass flow rate for laminar flow transition.*p*_{in}is the inlet pressure (*p*_{A}or*p*_{B}, depending on flow direction).*T*_{in}is the inlet temperature (*T*_{A}or*T*_{B}, depending on flow direction).

The proportionality constant is computed from the nominal flow conditions as

$${K}_{1}=\frac{\Delta {p}_{nom}{\rho}_{nom}}{{\dot{m}}_{nom}^{2}}$$

If the **Nominal mixture density** parameter is set to zero, then the
block computes the pressure drop as

$${p}_{A}-{p}_{B}={K}_{2}{\dot{m}}_{A}\sqrt{{\dot{m}}_{A}^{2}+{\left({f}_{lam}{\dot{m}}_{nom}\right)}^{2}}$$

where the proportionality constant is computed from the nominal flow conditions as

$${K}_{2}=\frac{\Delta {p}_{nom}}{{\dot{m}}_{nom}^{2}}$$

The flow resistance is assumed adiabatic, so the mixture specific total enthalpies are equal

$${h}_{A}+\frac{1}{2}\left(\frac{{\dot{m}}_{A}R{T}_{A}}{S{p}_{A}}\right)={h}_{B}+\frac{1}{2}\left(\frac{{\dot{m}}_{B}R{T}_{B}}{S{p}_{B}}\right)$$

The resistance is adiabatic. It does not exchange heat with the environment.

The pressure drop is assumed to be proportional to the square of the mixture mass flow rate and inversely proportional to the mixture density.