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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 v_{1}.

Figure 1, Compressible flow through a constriction.

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

$G=\frac{{A}_{2}}{\sqrt{1-({p}_{2}/{p}_{1}{)}^{2/k}({A}_{2}/{A}_{1}{)}^{2}}}\sqrt{\frac{2gk}{k-1}{p}_{1}{\gamma}_{1}[{\left(\frac{{p}_{2}}{{p}_{1}}\right)}^{2/k}-{\left(\frac{{p}_{2}}{{p}_{1}}\right)}^{(k+1)/k}]}$Eq. 2

$A}_{n}=\pi {\left(\frac{{d}_{n}}{2}\right)}^{2$where

*G* = weight flow rate, lbs/ft^{2}, (N/m^{2})

d_{1} = inlet area diameter, ft, (m)

d_{2} = inlet area diameter, ft, (m)

*A _{1}* = inlet area, ft

^{2}, (m

^{2})

*A*= constriction area, ft

_{2}^{2}, (m

^{2})

*g*= acceleration of gravity, ft/sec

^{2}(m/sec

^{2})

*k*= specific heat ratio

*p*= pressure inside the tank, lbs/ft

_{1}^{2}, (N/m

^{2})

*p*= pressure inside the tank, lbs/ft

_{2}^{2}, (N/m

^{2})

*γ*= specific weight of fluid inside the tank, lbs/ft

_{1}^{3}, (N/m

^{3})

R = Gas constant, ft/°R, (m/K)

Schaum's Outline of Fluid Mechanics and Hydraulics

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