Question

Pressure may be defined as the linear momentum per unit volume. Is it correct? Check with dim. Analysis.

Answer 1

Let us assume that pressure = linear momentum/volume
Pressure = mass* velocity   / volume (where momentum=mass*velocity)
Unit of Pressure = Kgm$s^{-1}$$m^{-3}$
or
Kg$s^{-1}$$m^{-2}$-----------------(1)

By the definition of pressure:
Pressure = Force/Area
Unit of pressure = Kgm$s^{-2}$$m^{-2}$
or
Kg$m^{-1} s^{-2}$----------------(2)

Since 1 is not equal to 2
Pressure is not a linear momentum per unit volume.

Answer 2

Dimensional formula of pressure = [ M¹ L⁻¹ T⁻² ]................(1)
Dimensional formula of momentum = [ M¹ L¹ T⁻¹ ]
Dimensional formula of volume = [ M° L³ T° ]

momentum / volume = [ M¹ L⁻² T⁻¹ ] .........................(2)
(1) ≠ (2)
Pressure can not be defined as the linear momentum per unit volume.