Dimensions of Pressure Gradient

Dimensional Formula of Pressure Gradient

The dimensional formula of pressure gradient is given by,

[M¹ L^-2 T^-2]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Pressure Gradient = Pressure × [Distance]^-1 . . . . (1)

The dimensional formula of distance = [M⁰ L¹ T⁰] . . . . (2)

⇒ Pressure = Force × [Area]^-1 . . . . (3)

Since, Force = mass × acceleration

∴ the dimensions of force = [M] × [L¹ T^-2] = [M¹ L¹ T^-2] . . . (4)

And, the dimensional formula of area = [M⁰ L² T⁰] . . . (5)

On substituting equation (4) and (5) in equation (3) we get,

Pressure (P) = [M¹ L¹ T^-2] × [M⁰ L² T⁰]^-1

Therefore, the dimensional formula of pressure = [M¹ L^-1 T^-2] . . . . (6)

On substituting equation (2) and (6) in equation (1) we get,

Pressure Gradient = Pressure × [Distance]^-1

Or, P = [M¹ L^-1 T^-2] × [M⁰ L¹ T⁰]^-1 = [M¹ L^-2 T^-2]

Therefore, the pressure gradient is dimensionally represented as [M¹ L^-2 T^-2].

⇒ Check Other Dimensional Formulas:

• Dimensions of Dipole Moment
• Dimensions of Kinematic Viscosity
• Dimensions of Weight
• Dimensions of Gravitational Potential Energy
• Dimensions of Time Period