Buoyant Force Dimensional Formula

Buoyant Force Dimensional Formula:

\[ [F_b] = [M L T^{-2}] \]

Buoyant Force Dimensional Value:

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1. What is Buoyant Force Dimensional Formula?

Definition: The dimensional formula for buoyant force is [M L T⁻²], representing its dependence on mass, length, and time.

Purpose: This formula helps analyze the fundamental dimensions of buoyant force in physical equations and unit conversions.

2. How Does the Dimensional Formula Work?

The dimensional formula is expressed as:

\[ [F_b] = [M L T^{-2}] \]

Where:

\( M \) — Mass (kilograms)
\( L \) — Length (meters)
\( T \) — Time (seconds)

Explanation: The formula shows buoyant force has dimensions of mass × length / time², equivalent to newtons (N) in SI units.

3. Importance of Dimensional Analysis

Details: Dimensional formulas help verify equations, convert between unit systems, and understand physical relationships.

4. Using the Calculator

Tips: Enter values for mass (kg), length (m), and time (s) to calculate the dimensional magnitude. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is buoyant force dimensionally equivalent to force?
A: Buoyant force is a type of force (like weight or tension), so it shares the same dimensional formula [M L T⁻²].

Q2: How does this relate to Archimedes' principle?
A: Archimedes' principle states buoyant force equals weight of displaced fluid, which also has dimensions [M L T⁻²].

Q3: What are the SI units for buoyant force?
A: The SI unit is newtons (N), where 1 N = 1 kg·m/s².

Q4: Can I use this for other types of forces?
A: Yes, all forces share the same dimensional formula [M L T⁻²].

Q5: How is this useful in fluid mechanics?
A: Dimensional analysis helps scale experiments and derive non-dimensional numbers like Reynolds number.