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Isentropic Flow of Fluid Equations and Calculator

Isentropic Flow of a Compressible Fluid Within a Conduit Equations and Calculator

Flow that is both adiabatic and frictionless is called isentropic flow. (Adiabatic means that no heat is transferred to the system from its surroundings or vice versa.) Isentropic flow exhibits no change in entropy. Isentropic flow is approximated in practice if the flow occurs very quickly (so there is little chance for heat transfer) and with a small amount of friction. Hence, isentropic analysis can be applied to high-velocity gas flow over short distances wherein friction and heat transfer should be relatively small.

Preview Isentropic Flow of Calculator

Isentropic flow can be analyzed by using the equations:

Eq. 1

${\displaystyle \frac{v_2^2-<!--\; -\; -->v_1^2}{2g}=\frac{p_1}{{\mathrm{\gamma <!--\; \gamma \; -->}}_1}\left(\frac{k}{k-<!--\; -\; -->1}\right)[1-<!--\; -\; -->{\left(\frac{p_2}{p_1}\right)}^{(k-<!--\; -\; -->1/k)}]}$

Eq. 2

${\displaystyle \frac{v_2^2-<!--\; -\; -->v_1^2}{2g}=\frac{p_2}{{\mathrm{\gamma <!--\; \gamma \; -->}}_2}\left(\frac{k}{k-<!--\; -\; -->1}\right)[{\left(\frac{p_1}{p_2}\right)}^{(k-<!--\; -\; -->1/k)}-<!--\; -\; -->1]}$

where:

v₂ = velocity at point 2, ft/sec (m/sec)
v₁ = velocity at point 1, ft/sec (m/sec)
p₂ = pressure at point 2, lbs/ft², (N/m²)
p₁ = pressure at point 1, lbs/ft², (N/m²)
k = specific heat ratio
γ₁ = specific weight at point 1
γ₂ = specific weight at point 2


The equation has some limitations that need to be pointed out. First of all, the equation should not be used for large pressure drops. Also, the pipe diameter must be constant, and pressure changes due to differences in elevation are considered negligible. Finally, it is limited to ordinary pressure ranges.

Approximate Properties of Some Gases [at 68° F (20°), 1 atm]

Gas	Specific Weight γ		Adiabaic Exponent k
	lb/ft3	N/m3
Air	0.0752	11.8	1.40
Ammonia	0.0448	7.0	1.32
Carbon Dioxide	0.1146	18.0	1.30
Methane	0.0416	6.5	1.32
Nitrogen	0.0726	11.4	1.40
Oxygen	0.0830	13.0	1.40
Sulfur dioxide	0.1695	26.6	1.26

Schaum's Outline of Fluid Mechanics and Hydraulics

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