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Isothermal Flow Compressible Fluid Within Conduit Equations and Calculator

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

Isothermal means at the same (or constant) temperature. Isothermal flow of a compressible fluid in a conduit occurs if heat transferred out of the fluid (through the conduit walls) and energy converted to heat by friction offset each other so that the temperature of the fluid is constant. This condition can occur in an uninsulated conduit with the same temperature inside and outside the conduit and with low velocities of fluid flowing in the conduit. Compressible fluid flow in long conduits can often be analyzed as isothermal flow.

Preview Isothermal Flow of a Compressible Fluid in Conduit Calculator

Isothermal flow in a pipe can be analyzed by using the following formula:

Eq. 1

${\displaystyle p_1^2-<!--\; -\; -->p_2^2=\frac{G^{2}RT}{g{A}^2}[f\frac{L}{D}+2\ln <!--\; ?\; -->\frac{p_1}{p_2}]}$

Eq. 2

${\displaystyle G^2=\frac{p_1^2-<!--\; -\; -->p_2^2}{(f\frac{L}{D}+2ln\frac{p_1}{p_2})}\frac{g{A}^2}{RT}}$

Eq. 3

A = π D² / 4 = π r²

where:

p₁ = pressure at point 1, lbs/ft², (N/m²)
p₂ = pressure at point 2, lbs/ft², (N/m²)
G = weight flow rate, lb/sec (N/sec)
R = gas constant, ft/°R (m/K)
T = absolute temperature of the fluid. °R
g = acceleration of gravity, ft/sec² (m/sec²)
A = cross-sectional area of the conduit, ft² (m²)
f = friction factor
L = length of segment from point 1 to point 2, , ft² (m²)
D = diameter of conduit, ft (m)

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		Gas Constant R
	lb/ft3	N/m3	ft/°R	m/K
Air	0.0752	11.8	53.3	29.3
Ammonia	0.0448	7.0	89.5	49.2
Carbon Dioxide	0.1146	18.0	34.9	19.2
Methane	0.0416	6.5	96.3	52.9
Oxygen	0.0830	13.0	48.3	26.6
Sulfur dioxide	0.1695	26.6	23.6	13.0

Schaum's Outline of Fluid Mechanics and Hydraulics

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