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 first principle of a free society is an untrammeled flow of words in an open forum.”
    —Adlai Stevenson (1900–1965)

    “Consciousness, we shall find, is reducible to relations between objects, and objects we shall find to be reducible to relations between different states of consciousness; and neither point of view is more nearly ultimate than the other.”
    —T.S. (Thomas Stearns)