In which of the following numbers gravitational force is the most significant?

Question

Question

This question was previously asked in

MPPSC AE Mechanical Official Paper (Held on 3 July 2022)

Answer 1

Concept: Various Numbers that are used for dimensional analysis are tabulated below.

Reynolds Number (Re)	\(\frac{Inertia~Force}{Viscous~force}\)	\(\frac{\rho VL}{\mu }\)
Froude Number (Fr)	\(\sqrt{\frac{Inertia~Force}{gravity~force}}\)	\(\frac{V}{\sqrt{gD}}\)
Euler Number (Eu)	\(\sqrt{\frac{Inertia~Force}{Pressure~force}}\)	\(\frac{V}{\sqrt{\frac{\text{ }\!\!\Delta\!\!\text{ }P}{\rho }}}\)
Newton Number (N)	\(\sqrt{\frac{Pressure~Force}{Inertia~force}}\)	\(\frac{\sqrt{\frac{\text{ }\!\!\Delta\!\!\text{ }P}{\rho }}}{V}\)
Mach Number (M)	\(\sqrt{\frac{Inertia~Force}{Elastic~force}}\)	\(\frac{V}{\sqrt{\frac{K}{\rho }}}\)
Weber Number (W)	\(\frac{Inertia~Force}{Surface~tension~force}\)	\(\frac{\rho {{V}^{2}}l}{\sigma }\)

Explanation:

Froude number is the ratio of inertial force to the gravitation force:

Froude number = \( \sqrt {\frac{{{f_i}}}{{{f_g}}}} = \frac{V}{{\sqrt {gd} }}\)

Where fi = inertial force, fg = gravitation force

So, for the Froude Number number, the gravitational force is the most significant.