Question

Froude's number is defined as the ratio of _____________

• A. inertia force to viscous force
• B. inertia force to gravity force
• C. inertia force to elastic force
• D. inertia force to pressure force

Hint:

To easily remember fluid dimensionless ratios:
- Reynolds \(\rightarrow\) Inertia Viscous
- Froude \(\rightarrow\) Inertia Gravity
- Mach \(\rightarrow\) Inertia Elastic
- Euler \(\rightarrow\) Inertia Pressure

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Dimensionless numbers are parameters used in fluid mechanics and open channel hydraulics to analyze flow behavior, perform model studies, and establish dynamic similarity between models and prototypes.
Key Formula or Approach:
The Froude Number (\(F_r\)) is mathematically defined as:
\[ F_r = \sqrt{\frac{\text{Inertia Force}}{\text{Gravity Force}}} = \frac{V}{\sqrt{gD}} \] Where:
- \(V\) is the flow velocity
- \(g\) is the acceleration due to gravity
- \(D\) is the hydraulic depth of the channel

Step 2: Detailed Explanation:
The Froude number represents the relative influence of inertial forces (which tend to keep the fluid moving) to gravitational forces (which resist changes in fluid elevation).
It is highly critical in open-channel hydraulics for classifying the state of flow:
- If \(F_r < 1\), the flow is subcritical (tranquil flow, governed by gravity forces).
- If \(F_r = 1\), the flow is critical.
- If \(F_r > 1\), the flow is supercritical (torrential/rapid flow, governed by inertia forces).
Let us review the other options:
- The ratio of inertia force to viscous force defines the Reynolds number (\(R_e\)).
- The ratio of inertia force to elastic force defines the Mach number (\(M\)).
- The ratio of inertia force to pressure force defines the Euler number (\(E_u\)).
Therefore, the Froude number is defined as the ratio of inertia force to gravity force.

Step 3: Final Answer:
Froude's number is defined as the ratio of inertia force to gravity force.