The dimensional formula of Pressure is [M¹L⁻¹T⁻²]. It is derived from the definition P = F/A (Pressure = Force per unit Area). Since force has dimensions [MLT⁻²] and area has dimensions [L²], pressure becomes [MLT⁻²]/[L²] = [ML⁻¹T⁻²]. The SI unit of pressure is Pascal (Pa), where 1 Pa = 1 N/m² = 1 kg·m⁻¹·s⁻².
Dimensional formula of Pressure = [M¹L⁻¹T⁻²].
Derived from P = F/A: [P] = [MLT⁻²]/[L²] = [ML⁻¹T⁻²].
SI unit of Pressure is Pascal (Pa); 1 Pa = 1 N/m² = 1 kg·m⁻¹·s⁻².
Standard atmospheric pressure = 101,325 Pa = 1 atm = 760 mmHg.
Stress, Young's Modulus, and Bulk Modulus all share the same dimensional formula [ML⁻¹T⁻²] as pressure.
Hydrostatic pressure P = ρgh confirms dimensions: [ML⁻³][LT⁻²][L] = [ML⁻¹T⁻²].
Pressure is a scalar quantity even though force is a vector.
Definition of Pressure: P = F / A
Where: • F = Force (SI unit: Newton, N) • A = Area (SI unit: m²)
Dimensions of each quantity: • [F] = [M¹L¹T⁻²] (dimensional formula of force) • [A] = [L²] (area = length × length)
Substituting into P = F/A: [P] = [M¹L¹T⁻²] / [L²] [P] = [M¹L¹⁻²T⁻²] [P] = [M¹L⁻¹T⁻²]
Dimensional Formula of Pressure = [M¹L⁻¹T⁻²]
SI unit verification: 1 Pascal = 1 N/m² = 1 kg·m·s⁻² / m² = 1 kg·m⁻¹·s⁻² This confirms the dimensional formula [M¹L⁻¹T⁻²] ✓
SI System: • Unit: Pascal (Pa) • 1 Pa = 1 N/m² = 1 kg·m⁻¹·s⁻² • Named after Blaise Pascal
CGS System: • Unit: Barye (Ba) • 1 Ba = 1 dyne/cm² = 0.1 Pa
Other commonly used units: • Atmosphere (atm): 1 atm = 101,325 Pa • Bar: 1 bar = 10⁵ Pa • mmHg (Torr): 1 mmHg = 133.322 Pa • psi (pounds per square inch): 1 psi ≈ 6894.76 Pa • kPa: 1 kPa = 1000 Pa • MPa: 1 MPa = 10⁶ Pa
Standard atmospheric pressure: 1 atm = 101,325 Pa ≈ 101.3 kPa ≈ 1.013 bar ≈ 760 mmHg
Pressure appears in many physical laws — all dimensionally consistent with [ML⁻¹T⁻²]:
Fluid Pressure (hydrostatic): P = ρgh [P] = [ML⁻³][LT⁻²][L] = [ML⁻¹T⁻²] ✓ (ρ = density, g = gravitational acceleration, h = depth)
Ideal Gas Law: PV = nRT → P = nRT/V [P] = [mol][J·mol⁻¹·K⁻¹][K]/[L³] = [ML²T⁻²]/[L³] = [ML⁻¹T⁻²] ✓
Bulk Modulus (B = -V·dP/dV): Bulk modulus has same dimensions as pressure [ML⁻¹T⁻²]
Young's Modulus (Y = stress/strain): Stress = Force/Area → [ML⁻¹T⁻²] (same as pressure) Strain is dimensionless, so [Y] = [ML⁻¹T⁻²]
Comparing Force and Pressure:
Force: • Dimensional formula: [MLT⁻²] • SI unit: Newton (N) • Direction: vector quantity • Does not depend on area
Pressure: • Dimensional formula: [ML⁻¹T⁻²] • SI unit: Pascal (Pa) • Direction: scalar quantity (acts in all directions in fluids) • Depends on area: larger area → smaller pressure for same force
Key differences in exponents: • Force: L¹ (positive power of length) • Pressure: L⁻¹ (negative power of length — because dividing by area L²)
Practical Example: A stiletto heel (small area) exerts much greater pressure than a flat shoe (large area) even with the same weight (force).
Quantities with same dimensional formula as pressure [ML⁻¹T⁻²]: • Stress (mechanical) • Young's Modulus • Bulk Modulus • Shear Modulus • Energy density (energy per unit volume)
Pressure applications: • Atmospheric pressure measured by barometer • Blood pressure in medicine (measured in mmHg) • Tyre pressure in vehicles (measured in psi or bar) • Water pressure in hydraulic systems • Gas pressure in thermodynamics (PV = nRT)
Pascal's Law: Pressure applied to a confined fluid is transmitted equally in all directions. This is the principle behind hydraulic brakes, hydraulic lifts, and hydraulic presses.
[M¹L⁻¹T⁻²]. Derived from P = F/A: [P] = [MLT⁻²]/[L²] = [ML⁻¹T⁻²].
Pascal (Pa). 1 Pa = 1 N/m² = 1 kg·m⁻¹·s⁻².
[ML⁻¹T⁻²] — same as pressure, since stress = Force/Area.
1 atm = 101,325 Pa ≈ 101.3 kPa. It is also equal to 760 mmHg or approximately 1.013 bar.
Force: [MLT⁻²] (L has positive power). Pressure: [ML⁻¹T⁻²] (L has negative power, due to dividing by area L²).
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