Water Quality Engine Technical Manual - Working Draft for Review Reservoir Hydraulics Current: Equation of State PDF Download PDF Download page Equation of State. Current page All pages Equation of State In the HEC-Water Quality Engine, an equation of state is used to calculate the density of fresh water (\rho_{\textrm{fw}}) as a function of water temperature (T) : \rho_{\textrm{fw}} = 999.842594 + 6.793952 \times 10^{-2} T - 9.095290 \times 10^{-3} T^2 + 1.001685 \times 10^{-4} T^3 - 1.120083 \times 10^{-6} T^4 + 6.536332 \times 10^{-9} T^5 For simulations with salinity (S) modeled, this equation is modified to also include its impact on density: \rho_{\textrm{sw}}=\rho_{\textrm{fw}} + a S + b S^{1.5} + c S^2 \newline a = 8.24493 \times 10^{-1} - 4.0899 \times 10^{-3} T + 7.6438 \times 10^{-5} T^2 - 8.2467 \times 10^{-7} T^3 + 5.3875 \times 10^{-9} T^4 \newline b = -5.72466 \times 10^{-3} + 1.0227 \times 10^{-4} T - 1.6546 \times 10^{-6} T^2 \newline c = 4.8314 \times 10^{-4} In these equations, the density of water is given in units of kg/m3, salinity in ppt, and temperature in °C (Millero and Poisson, 1981). ×