Reynold's number is the ratio of

Number

Definition

Significance

Reynolds No

\(Re = \frac{{Inertia\;Force}}{{Viscous\;Force}} \)

\(Re =\frac{{\rho VL}}{\mu }\)

Flow in closed conduit i.e. flow through pipes.

Froude No

\(Fr = \sqrt {\frac{{Inertia\;Force}}{{Gravity\;Force}}} \)

\(Fr = \frac{V}{{\sqrt {gL} }}\)

Where a free surface is present and gravity force is predominant.

Spillway, Open Channels, waves in the ocean.

Euler No.

\({E_u} = \sqrt {\frac{{Inertia\;Force}}{{Pressure\;Force}}} \)

\({E_u} =\frac{V}{{\sqrt {\frac{p}{\rho }} }}\)

In cavitation studies, where pressure force is predominant.

Mach No.

\(M = \sqrt {\frac{{Inertia\;Force}}{{Elastic\;Force}}} \)

\(M = \frac{V}{C}\)

Where fluid compressibility is important.

Launching of rockets, airplanes and projectile moving at supersonic speed.

Weber No.

\({W_e} = \sqrt {\frac{{Inertia\;Force}}{{Surf\;tension\;Force}}} \)

\({W_e} =\frac{V}{{\sqrt {\frac{\sigma }{{\rho L}}} }}\)

In Capillary studies i.e. where Surface tension is predominant.