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Compressible Flow through a Constriction Equations and Calculator

Compressible Flow through a Constriction Equations and Calculator

Figure 1 depicts compressible fluid flow through a constriction in a conduit. The various parameters are shown at point 1 in the larger section and point 2 in the smaller section. This configuration is similar to the convergent nozzle (Fig. 2), but it differs because the cross section at point 1 is generally not large enough to neglect velocity v₁.

Figure 1, Compressible flow through a constriction.

Figue 2, Convergent nozzle.

Preview Compressible Flow through a Constriction Calculator

The weight flow rate for compressible flow through a constriction can be determined from the equation

Eq. 1

${\displaystyle G=\frac{A_2}{\sqrt{1-<!--\; -\; -->(p_2/p_1{)}^{2/k}(A_2/A_1{)}^2}}\sqrt{\frac{2gk}{k-<!--\; -\; -->1}{p}_1{\mathrm{\gamma <!--\; \gamma \; -->}}_1[{\left(\frac{p_2}{p_1}\right)}^{2/k}-<!--\; -\; -->{\left(\frac{p_2}{p_1}\right)}^{(k+1)/k}]}}$

Eq. 2

${\displaystyle A_n=\mathrm{\pi <!--\; \pi \; -->}{\left(\frac{d_n}{2}\right)}^2}$

where

G = weight flow rate, lbs/ft², (N/m²)
d₁ = inlet area diameter, ft, (m)
d₂ = inlet area diameter, ft, (m)
A₁ = inlet area, ft², (m²)
A₂ = constriction area, ft², (m²)
g = acceleration of gravity, ft/sec² (m/sec²)
k = specific heat ratio
p₁ = pressure inside the tank, lbs/ft², (N/m²)
p₂ = pressure inside the tank, lbs/ft², (N/m²)
γ₁ = specific weight of fluid inside the tank, lbs/ft³, (N/m³)
R = Gas constant, ft/°R, (m/K)

Schaum's Outline of Fluid Mechanics and Hydraulics

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