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, .
Conservation of enthalpy leads to velocity, , at the vent hole. The Bernouilli equation is then written as:
Applying the adiabatic conditions:
Therefore, the exit velocity is given by:
with the averaged density of the gas and the fraction of massic averages of heat capacities at constant pressure and constant volume.
The mass flow rate is given by:
The energy flow rate is given by:
The total mass flow rate is given by:
- 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
Vent pressure is equal to external pressure for unshocked flow. For shocked flow, is equal to critical pressure and is bounded to critical sound speed:
And,
Outgoing Mass per Gas
The mass flow of gas is , where is the volume occupied by gas and satisfies:
(from and ).
It comes finally