1/19/2024 0 Comments Force-tank max![]() So you can solve for $M(v_g)$ and substitute in the above equations and solve for $v_g$ self-consistently. ![]() The rate at which mass leaves is a function of the exit velocity (it depends on the volumetric flow rate, which is a product of the exit orifice size and the exit velocity). This is a function of time because mass is leaving the tank. Where $m$ is the molecular mass of the gas in question, $T$ the temperature, $R$ the gas constant, and $M$ the total mass of the gas remaining in the tank. If you assume the tank remains at a constant ambient temperature, the pressure will only vary with the mass flow rate (isothermal expansion) and you can obtain that from the ideal gas law: If the tank is a rigid container (like a propane tank) then the volume of the gas is constant and the pressure will vary with the mass flow and the temperature. The gas density $\rho_g \equiv M / V$ is the ratio of the mass of gas (M) in the tank to the volume of the tank. Where the $g$ subscripts pertain to the gas and the $a$ subscript to the ambient. If you neglect viscosity, Bernoulli's equation (just Navier-Stokes without frictional or stress terms) will get you into the ballpark:
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