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}

Read more about this topic:  Rayleigh Flow

Famous quotes containing the words additional, flow and/or relations:

    “When I turned into a parent, I experienced a real and total personality change that slowly shifted back to the “normal” me, yet has not completely vanished. I believe the two levels are now superimposed, with an additional sprinkling of mortality intimations.”
    —Sonia Taitz (20th century)

    “The current of our thoughts made as sudden bends as the river, which was continually opening new prospects to the east or south, but we are aware that rivers flow most rapidly and shallowest at these points.”
    —Henry David Thoreau (1817–1862)

    “What a man sows, that shall he and his relations reap.”
    —Clarissa Graves (1892–1985?)