Chocked/Unchocked Flow

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Choked flow is a compressible flow effect. The parameter that becomes "choked" or "limited" is the mass flow rate. Choked flow is a fluid dynamic condition associated with the Venturi effect. When a flowing fluid at a given pressure and temperature passes through a restriction (such as the throat of a convergent-divergent nozzle or a valve in a pipe) into a lower pressure environment the fluid velocity increases. At initially subsonic upstream conditions, the conservation of mass principle requires the fluid velocity to increase as it flows through the smaller cross-sectional area of the restriction. At the same time, the Venturi effect causes the static pressure, and therefore the density, to decrease downstream past the restriction. Choked flow is a limiting condition which occurs when the mass flow rate will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed.Wikipedia

Choked/Unchoked Flow:

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Critical Pressure Ratio =

\small \bold{\color{blue} R_{crit} = { \left ( \frac{2}{k+1} \right ) }^{ \frac{k}{k-1}}}

k = Heat Capacity Ratio = Adiabatic Index = γ
k usually in the range 1.09 to 1.67.

\small \bold{\color{blue} k = \gamma = \frac{c_p}{c_v}}

Inlet Pressure (in absolute Pa) = Pin
Outlet Pressure (in absolute Pa) = Pout
Flow is CHOKED or critical if

\small \bold{\color{blue} R_{crit} \geq \frac {P_{out}}{P_{in}}}

Flow is UNCHOKED or subcritical if

\small \bold{\color{blue} R_{crit} < \frac {P_{out}}{P_{in}}}

Enter absolute inlet pressure and outlet pressure and heat capacity ratio (k) in below input boxes.

Pin Inlet Pressure (absolute Pa):
Pout Outlet Pressure (absolute Pa):
Heat Capacity Ratio (k):

Critical Pressure Ratio (Rcrit):

Absolute Pressure Ratio:

Under this condition, the flow is:

\small \bold{\color{blue} \dot{m} = CA \ \sqrt[]{k \rho_{in} P_{in} { \left ( \frac{2}{k+1} \right ) }^{ \frac{k}{k-1}}} \ = \ CAP_{in} \ \sqrt[]{\left ( \frac{kM}{Z_{in} RT_{in}} \right ) { \left ( \frac{2}{k+1} \right ) }^{ \frac{k}{k-1}}} }

\small {\color{black} \dot{m} } = mass flow rate, kg/s
\small {\color{black} C } = discharge coefficient, dimensionless, usually 0.72.
\small {\color{black} A } = discharge hole cross-sectional area, m2.
\small {\color{black} \rho_{in}} = real gas (total) density at total pressure Pin and total temperature Tin, kg/m3.
\small {\color{black} T_in } = absolute upstream total temperature of the gas, K.
\small {\color{black} M } = gas molecular weight (dimensionless).
\small {\color{black} R } = Universal Gas Law constant, (Pa.m3) / (kgmol.K) = 8.314472.103.
\small {\color{black} Z_{in}} = the gas compressibility factor at Pin and Tin. Ideal gas Zin = 1.

To calculate the choke flow, please enter (C, A and ρin) or (C, A, M, Zin, and Tin)

Discharge Coefficient (C):
Hole Cross-sectional area (A):
Variable(s) to be inputed:

M, Zin and Tin
Density at Pin and Tinin)

Choked Mass Flow Rate (m):

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