What is the dimension of a pressure gradient?

The dimension of a pressure gradient is [M¹ L^-2 T^-2], where M represents Mass, L represents Length, and T represents Time.

Understanding Pressure Gradient Dimensions

A pressure gradient describes how pressure changes across a distance. It is a vector quantity indicating the direction and rate of the most rapid pressure increase.

Here's a breakdown of why the dimensional formula is [M¹ L^-2 T^-2]:

• Pressure: Pressure itself has dimensions of force per unit area. Force (F) is mass (M) times acceleration (L/T²), so F is [MLT^-2]. Area is L². Therefore, pressure is [MLT^-2] / [L²] = [M¹ L^-1 T^-2].
• Gradient: A gradient involves a change in some quantity divided by a change in distance (length). Thus, the pressure gradient involves dividing the pressure dimension by the length dimension.
• Pressure Gradient Dimension: This calculation leads to:
  [M¹ L^-1 T^-2] / [L¹] = [M¹ L^-2 T^-2].

Dimension	Symbol	Explanation
Mass	M	Units like kg
Length	L	Units like meters
Time	T	Units like seconds

Therefore, the dimensional formula for pressure gradient is confirmed to be [M¹ L^-2 T^-2], based on the provided reference.