Fanno Flow - Additional Fanno Flow Relations

Additional Fanno Flow Relations

As was stated earlier, the area and mass flow rate in the duct are held constant for Fanno flow. Additionally, the stagnation temperature remains constant. These relations are shown below with the * symbol representing the throat location where choking can occur. A stagnation property contains a 0 subscript.

begin{align} A &= A^* = mbox{constant} \ T_0 &= T_0^* = mbox{constant} \ dot{m} &= dot{m}^* = mbox{constant} end{align}

Differential equations can also be developed and solved to describe Fanno flow property ratios with respect to the values at the choking location. The ratios for the pressure, density, temperature, velocity and stagnation pressure are shown below, respectively. They are represented graphically along with the Fanno parameter.

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

Read more about this topic:  Fanno Flow

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

    “When one walks, one is brought into touch first of all with the essential relations between one’s physical powers and the character of the country; one is compelled to see it as its natives do. Then every man one meets is an individual. One is no longer regarded by the whole population as an unapproachable and uninteresting animal to be cheated and robbed.”
    —Aleister Crowley (1875–1947)

    “For as the interposition of a rivulet, however small, will occasion the line of the phalanx to fluctuate, so any trifling disagreement will be the cause of seditions; but they will not so soon flow from anything else as from the disagreement between virtue and vice, and next to that between poverty and riches.”
    —Aristotle (384–322 B.C.)

    “The world will never be long without some good reason to hate the unhappy; their real faults are immediately detected, and if those are not sufficient to sink them into infamy, an additional weight of calumny will be superadded.”
    —Samuel Johnson (1709–1784)