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Standardized Equation for Hydrogen Gas Densities for Fuel Consumption Applications



Eric Lemmon, Marcia L. Huber, Daniel G. Friend, Carl Paulina


One of three currently recognized methods for evaluating the consumption of gaseous hydrogen fuel in vehicle applications involves the determination of the equilibrium temperature and pressure of the gas before and after usage within a storage tank of known, and essentially fixed, volume. This method requires the density of hydrogen. A current standard for the thermodynamic properties of hydrogen is provided by a 32-term equation of state, in which the pressure is given as a function of density and temperature. In some fuel consumption applications, this form is inconvenient to use since the equation must be solved in an iterative manner in order to provide the density in terms of pressure and temperature. In order to easily calculate gaseous hydrogen fuel consumption in vehicle applications in which temperature and pressure are measured, we have established an equation for the density of hydrogen gas which agrees with the current standard to within 0.01% from 220 to 400 K with pressures from 0 to 45 MPa. The equation is a truncated virial-type equation in terms of pressure, and temperature-dependent pressure virial coefficients, with terms up to order 5. The density uncertainty for this equation is the same as the current standard and is estimated as 0.2% (combined uncertainty with a coverage factor of 2) over this range. Comparisons are presented with experimental data and with the full 32-term equation of state.
Proceedings Title
Proc. SAE World Congress
Conference Dates
April 3-4, 2006
Conference Location
Detroit, MI, USA
Conference Title
SAE World Congress 2006


density, hydrogen, virial equation


Lemmon, E. , Huber, M. , Friend, D. and Paulina, C. (2006), Standardized Equation for Hydrogen Gas Densities for Fuel Consumption Applications, Proc. SAE World Congress, Detroit, MI, USA, [online], (Accessed February 29, 2024)
Created April 2, 2006, Updated October 12, 2021