Cauchy Number
Cauchy number, abbreviated as Ca, a dimensionless number, is the ratio of inertial force to compressibility force in a flow. When the compressibility is important the elastic forces must be considered along with inertial forces.
The Cauchy number provides a measure of the importance of viscous effects compared to inertial effects in a fluid flow. It helps determine the behavior of the flow, such as whether it is dominated by viscous forces (low Cauchy number) or inertial forces (high Cauchy number).
Cauchy Number formula |
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| \(\large{ Ca = \frac{v^2 \; \rho }{ B } }\) | ||
Cauchy Number - Solve for Ca\(\large{ Ca = \frac{v^2 \; \rho }{ B } }\)
Cauchy Number - Solve for v\(\large{ v = \sqrt{ \frac{Ca \; B }{ p } } }\)
Cauchy Number - Solve for p\(\large{ p = \frac{ Ca \; B }{ v^2 } }\)
Cauchy Number - Solve for B\(\large{ B = \frac{ v^2 \; p }{ Ca } }\)
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| Symbol | English | Metric |
| \(\large{ Ca }\) = Cauchy number | \(\large{dimensionless}\) | |
| \(\large{ v }\) = velocity of the flow | \(\large{\frac{ft}{sec}}\) | \(\large{\frac{m}{s}}\) |
| \(\large{ \rho }\) (Greek symbol rho) = density | \(\large{\frac{lbm}{ft^3}}\) | \(\large{\frac{kg}{m^3}}\) |
| \(\large{ B }\) = bulk modulus elasticity | \(\large{\frac{lbm}{in^2}}\) | \(\large{Pa}\) |
Tags: Force Equations