When a fluid flows from one location (“start”) to another location (“end”) under certain circumstances, the changes in fluid properties can be described by the Bernoulli equation, which is

where
α = a dimensionless correction factor
ρ = fluid density
P = fluid pressure
ν = fluid velocity
z = fluid elevation
g = acceleration of gravity

Prove that this equation is dimensionally consistent in both the American engineering system and the metric system.

Pstart - Pend P + -a (Vstart-Vend) + 8 (Zstart Zend) = 0