1. What is the Dimensional Formula of Pressure?

Definition: The dimensional formula of pressure represents its physical quantity in terms of fundamental dimensions: mass (M), length (L), and time (T).

Purpose: It helps in understanding the nature of pressure and in verifying the correctness of physical equations involving pressure through dimensional analysis.

2. How is the Dimensional Formula Derived?

The dimensional formula is derived from the pressure formula:

Where:

• \( P \) — Pressure
• \( F \) — Force (dimensional formula [M L T⁻²])
• \( A \) — Area (dimensional formula [L²])

Explanation: Substituting the dimensional formulas of force and area gives [M L T⁻²]/[L²] = [M L⁻¹ T⁻²].

3. Importance of Dimensional Formula

Details: The dimensional formula helps in:

• Checking the consistency of physical equations
• Deriving relationships between physical quantities
• Converting units between different systems
• Understanding the nature of the physical quantity

4. Base Quantities Explained

The fundamental dimensions are:

• M — Mass (measured in kilograms, kg)
• L — Length (measured in meters, m)
• T — Time (measured in seconds, s)

5. Frequently Asked Questions (FAQ)

Q1: What does the negative exponent in L⁻¹ mean?
A: It indicates an inverse relationship with length. Pressure decreases as area (length squared) increases.

Q2: How does this relate to SI units of pressure?
A: The SI unit Pascal (Pa) is kg·m⁻¹·s⁻², which matches the dimensional formula.

Q3: Can this formula be used for fluid pressure?
A: Yes, the dimensional formula applies to all types of pressure - fluid, gas, or mechanical.

Q4: Why isn't temperature included in the formula?
A: In basic dimensional analysis, temperature is only needed for thermodynamic systems.

Q5: How would this change in other unit systems?
A: The dimensional formula remains the same, though the base units would differ (e.g., pounds, feet, seconds in FPS system).