Engineering Fluid Dynamics: Proof of the Static Pressure Head equation

[PaxFinnica96]

Homework Statement

A horizontal pipe is filled with liquid. When the liquid is stationary, its head H metres depends on the pressure p of the liquid, its density ρ and gravitational acceleration g. Determine the nature of the relationship of these variables.

Relevant Equations

H = p/ρg

Where:
H = Head
p = Pressure
ρ = density
g = gravitational acceleration

I am trying to mathematically prove the Static Pressure Head equation:

H = p/ρg

How can I prove this equation and thus determine the nature of the relationship between these variables?

 

[Lnewqban]

P (N/m2) and H (m) are equivalent magnitudes.
Rho and g make those two dimensionally compatible.

 

[jack action]

https://en.wikipedia.org/wiki/Bernoulli's_principle#Derivations_of_the_Bernoulli_equation

Look at the section Derivation by using conservation of energy.