Bernoulli's equation shows that in frictionless flows the sum of kinetic, potential and pressure energy is constant along a streamline. For gases, the geodetic pressure component can be neglected if no significant height differences occur:
p_{\mathrm{tot}}=p+p_{\mathrm{d}}=p+\frac{\rho}{2}\cdot v^2=\mathrm{const.}
Figure 2.5.: Bernoulli's Equation
Taking friction (pressure losses) into account, the following equation is obtained for Figure 2.5:
p_{\mathrm{I}}+\frac{\rho_{\mathrm{I}}}{2}\cdot v_{\mathrm{I}}^2=p_{\mathrm{II}}+\frac{\rho_{\mathrm{II}}}{2}\cdot v_{\mathrm{II}}^2+\Delta p_{\mathrm{V,I-II}}=p_{\mathrm{III}}+\frac{\rho_{\mathrm{III}}}{2}\cdot v_{\mathrm{III}}^2+\Delta p_{\mathrm{V,II-III}}
\Delta p_V: Pressure loss