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Generate time-varying pressure differential

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

The Controlled Pressure Source (MA) block represents an
ideal mechanical energy source in a moist air network. The pressure differential is
controlled by the input physical signal at port **P**. The source can
maintain the specified pressure differential across its ports regardless of the mass
flow rate through the source. There is no flow resistance and no heat exchange with the
environment. A positive signal at port **P** causes the pressure at
port **B** to be greater than the pressure at port
**A**.

The equations describing the source use these symbols.

c_{p} | Specific heat at constant pressure |

h | Specific enthalpy |

h_{t} | Specific total enthalpy |

$$\dot{m}$$ | Mass flow rate (flow rate associated with a port is positive when it flows into the block) |

p | Pressure |

ρ | Density |

R | Specific gas constant |

s | Specific entropy |

T | Temperature |

Φ_{work} | Power delivered to the moist air flow through the source |

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:

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

If the source performs no work (**Power added** parameter is set to
`None`

), then $${\Phi}_{work}=0$$.

If the source is isentropic (**Power added** parameter is set to
`Isentropic power`

), then

$${\Phi}_{work}={\dot{m}}_{A}\left({h}_{tB}-{h}_{tA}\right)$$

where

$$\begin{array}{l}{h}_{tA}={h}_{A}+\frac{1}{2}{\left(\frac{{\dot{m}}_{A}}{{\rho}_{A}{S}_{A}}\right)}^{2}\\ {h}_{tB}={h}_{B}+\frac{1}{2}{\left(\frac{{\dot{m}}_{B}}{{\rho}_{B}{S}_{B}}\right)}^{2}\end{array}$$

The mixture-specific enthalpies, *h*_{A} =
*h*(*T*_{A}) and
*h*_{B} =
*h*(*T*_{B}), are constrained by
the isentropic relation, that is, there is no change in entropy:

$${\int}_{{T}_{A}}^{{T}_{B}}\frac{1}{T}}dh\left(T\right)=R\mathrm{ln}\left(\frac{{p}_{B}}{{p}_{A}}\right)$$

The quantity specified by the input signal of the source is

$${p}_{B}-{p}_{A}=\Delta {p}_{specified}$$

There are no irreversible losses.

There is no heat exchange with the environment.