What is the dimensionless ratio between fluid inertial forces and fluid gravitational forces?

What is the dimensionless ratio between fluid inertial forces and fluid gravitational forces?

• A. Froude Number
• B. Reynolds Number
• C. Mach Number
• D. Weber Number

Answer: (A)

The main idea is to compare how strongly inertia drives the flow relative to gravity pulling on the fluid. This comparison is captured by the Froude number, defined as Fr = V / sqrt(gL), where V is a characteristic velocity, L a characteristic length, and g gravity. This ratio comes from comparing inertial effects (acceleration scales like V^2/L) to gravitational acceleration g. The Froude number tells you which force dominates: if Fr is much less than 1, gravity governs the motion (as in shallow or slow flows); if Fr is much greater than 1, inertial effects dominate (as in rapid, large-scale flows). Other dimensionless numbers relate to different comparisons: Reynolds number compares inertia to viscous forces, Mach number compares flow speed to the speed of sound, and Weber number compares inertia to surface tension.

The main idea is to compare how strongly inertia drives the flow relative to gravity pulling on the fluid. This comparison is captured by the Froude number, defined as Fr = V / sqrt(gL), where V is a characteristic velocity, L a characteristic length, and g gravity.

This ratio comes from comparing inertial effects (acceleration scales like V^2/L) to gravitational acceleration g. The Froude number tells you which force dominates: if Fr is much less than 1, gravity governs the motion (as in shallow or slow flows); if Fr is much greater than 1, inertial effects dominate (as in rapid, large-scale flows).

Other dimensionless numbers relate to different comparisons: Reynolds number compares inertia to viscous forces, Mach number compares flow speed to the speed of sound, and Weber number compares inertia to surface tension.