Dimensions and Units used in Fluid Mechanics - Dimensional Homogeneity

Key Concept: The basic equations in fluid mechanics must be dimensionally homogeneous.

In short, each term in an equation must have the same dimensions and the dimensions on one

side of the equal sign must be the same as on the other side. If not, the resulting equation is

in error and you should closely examine the steps you took to arrive at this equation.

Physical Quantity	Symbol	FLT System
Mass Density	ρ	FT^2/L^4
Pressure	P	F/L^2
Gravity	g	L/T^2

Example: Check to see if P = ρ g h is dimensionally homogeneous where P is fluid

pressure, ρ is mass density, g is the acceleration of gravity, and h is the height

of a column of fluid

Strategy: Enter the dimensions for each term in the equation (on both sides).

P = ρ g h

F/L² = FT²/L⁴ L/T² L

F/L² = [ FT²/L⁴ ] [ L/T² ] [ L] = F/L²

Therefore P = ρ g h is dimensionally homogeneous and is a possible correct result.

Example: If instead you arrived at the equation P = ρ g h²

Your check on dimensional homogeneity would yield F/L² = F/L

And your equation P = ρ g h² cannot be a correct result.

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