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Reference.org
Dynamic similarity (Reynolds and Womersley numbers)
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<p>In <a href="/facts/Fluid_mechanics/NIy4tRfE">fluid mechanics</a>, dynamic similarity is the phenomenon that when there are two geometrically similar vessels (same shape, different sizes) with the same boundary conditions (e.g., no-slip, center-line velocity) and the same <a href="/facts/Reynolds_number/4sdungsf">Reynolds</a> and <a href="/facts/Womersley_number/wAz04RbL">Womersley numbers</a>, then the fluid flows will be identical. This can be seen from inspection of the underlying <a href="/facts/Navier-Stokes_equation/48pQugEa">Navier-Stokes equation</a>, with geometrically similar bodies, equal Reynolds and Womersley Numbers the functions of velocity (u’,v’,w’) and pressure (P’) for any variation of flow. </p>