Rayleigh Flow - Additional Rayleigh Flow Relations

Additional Rayleigh Flow Relations

The area and mass flow rate are held constant for Rayleigh flow. Unlike Fanno flow, the Fanning friction factor, f, remains constant. These relations are shown below with the * symbol representing the throat location where choking can occur.

\begin{align} A &= A^* = \mbox{constant} \\ \dot{m} &= \dot{m}^* = \mbox{constant} \\ \end{align}

Differential equations can also be developed and solved to describe Rayleigh flow property ratios with respect to the values at the choking location. The ratios for the pressure, density, static temperature, velocity and stagnation pressure are shown below, respectively. They are represented graphically along with the stagnation temperature ratio equation from the previous section. A stagnation property contains a '0' subscript.

\begin{align} \frac{p}{p^*} &= \frac{\gamma + 1}{1 + \gamma M^2} \\ \frac{\rho}{\rho^*} &= \frac{1 + \gamma M^2}{\left(\gamma + 1\right)M^2} \\ \frac{T}{T^*} &= \frac{\left(\gamma + 1\right)^2M^2}{\left(1 + \gamma M^2\right)^2} \\ \frac{V}{V^*} &= \frac{\left(\gamma + 1\right)M^2}{1 + \gamma M^2} \\ \frac{p_0}{p_0^*} &= \frac{\gamma + 1}{1 + \gamma M^2}\left^\frac{\gamma}{\gamma - 1} \end{align}

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