What is the dimensional formula of the pressure head?

The pressure head is a measure of the potential energy per unit weight of fluid. It is typically defined as the pressure divided by the density of the fluid and the acceleration due to gravity. The dimensional formula of pressure head can be derived as follows:

Pressure (P) has the dimensional formula: [M][L]^-1[T]^-2 (mass per unit area per unit time squared)
Density (ρ) has the dimensional formula: [M][L]^-3 (mass per unit volume)
Acceleration due to gravity (g) has the dimensional formula: [L][T]^-2 (length per unit time squared)

Therefore, the dimensional formula of pressure head can be calculated by dividing the dimensional formula of pressure by the product of the dimensional formulas of density and acceleration due to gravity:

[P] / ([ρ][g]) = ([M][L]^-1[T]^-2) / ([M][L]^-3 * [L][T]^-2)

Simplifying the expression:

[M][L]^-1[T]^-2 / ([M][L]^-3 * [L][T]^-2)
= [M][L]^-1[T]^-2 * [L]^3 * [T]^2
= [M][L]^2[T]^-1

Therefore, the dimensional formula of pressure head is [M][L]^2[T]^-1 (mass times length squared per unit time).