Which dimensionless number measures the ratio of inertial to gravitational forces?

Which dimensionless number measures the ratio of inertial to gravitational forces?

• A. The ratio of Reynolds to Mach
• B. The ratio of viscous to inertial forces
• C. The ratio of inertial to gravitational forces
• D. The ratio of gravitational to inertial forces

Answer: (C)

When you compare inertial effects to gravity in a flow, you’re looking at how strong inertia is relative to gravity, which is captured by the Froude number. If you take a characteristic velocity U and length L, inertial forces scale as ρU^2/L while gravitational forces scale as ρg. The ratio of these two scales gives Fr = U^2/(gL). This dimensionless number tells you whether inertia dominates gravity (Fr large) or gravity dominates inertia (Fr small). The expression described—ratio of inertial to gravitational forces—directly corresponds to this Fr quantity. The other options mix in Reynolds or Mach numbers or describe the inverse ratio, so they don’t represent the inertial-to-gravity comparison in the same way.

When you compare inertial effects to gravity in a flow, you’re looking at how strong inertia is relative to gravity, which is captured by the Froude number. If you take a characteristic velocity U and length L, inertial forces scale as ρU^2/L while gravitational forces scale as ρg. The ratio of these two scales gives Fr = U^2/(gL). This dimensionless number tells you whether inertia dominates gravity (Fr large) or gravity dominates inertia (Fr small). The expression described—ratio of inertial to gravitational forces—directly corresponds to this Fr quantity. The other options mix in Reynolds or Mach numbers or describe the inverse ratio, so they don’t represent the inertial-to-gravity comparison in the same way.