# Venting Outgoing Mass Determination

Venting, or the expulsion of gas from the airbag, is assumed to be isenthalpic.

The flow is also assumed to be unshocked, coming from a large reservoir and through a small orifice with effective surface area, $T$ .

Conservation of enthalpy leads to velocity, $u$ , at the vent hole. The Bernouilli equation is then written as:

(airbag) $\frac{\gamma}{\gamma -1}\frac{P}{\rho}=\frac{\gamma}{\gamma -1}\frac{{P}_{ext}}{{\rho}_{vent}}+\frac{{u}^{2}}{2}$ (vent hole)

(airbag) $\frac{P}{{\rho}^{\gamma}}=\frac{{P}_{ext}}{{\rho}_{vent}{}^{\gamma}}$ (vent hole)

with $\rho =\frac{{\displaystyle \sum _{i}{m}^{(i)}}}{V}$ the averaged density of the gas and $\gamma =\frac{\left[{\displaystyle \sum _{i}{m}^{(i)}}{c}_{p}{}^{(i)}\right]/\left[{\displaystyle \sum _{i}{m}^{(i)}}\right]}{\left[{\displaystyle \sum _{i}{m}^{(i)}}{c}_{v}{}^{(i)}\right]/\left[{\displaystyle \sum _{i}{m}^{(i)}}\right]}$ the fraction of massic averages of heat capacities at constant pressure and constant volume.

- ${A}_{vent}$
- Vent hole surface.

- a constant area taking into account a discharge coefficient
- a variable area equal to the area of a specified surface multiplied by a discharge coefficient.

## Supersonic Outlet Flow

And,

${P}_{crit}=P{\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma}{\gamma -1}}$

${P}_{vent}=\mathrm{max}\left({P}_{crit},{P}_{ext}\right)$

## Outgoing Mass per Gas

The mass flow of gas $i$ is $d{m}^{(i)}{}_{out}=\frac{{V}^{(i)}}{V}d{m}_{out}$ , where ${V}^{(i)}$ is the volume occupied by gas $i$ and satisfies:

${V}^{(i)}=\frac{{n}^{(i)}}{n}V$ (from $P{V}^{(i)}={n}^{(i)}RT$ and $PV=\left[{\displaystyle \sum _{i}{n}^{(i)}}\right]RT$ ).