Dimensional Analysis in Fluid Mechanics (continued)

The table below lists important dimensionless products appearing in fluid mechanics as

well as indicating the important forces that each product represents.

Reynolds Number	Re = VDρ/μ	inertial force/viscous force
Weber Number	We = ρV^2L/σ	inertial force / surface tension force
Froude Number	Fr = V/√gL	inertial force / gravitational force
Mach Number	Ma = V/C	inertial force / compressibility force
Euler Number	Eu = p / ρV^2	pressure force / inertial force

Variable Definition F-L-T Dimensions M-L-T

V	Fluid velocity (speed)	L/T	L/T
ρ	Fluid density	FT^2/L^4	M/L^3
μ	Dynamic viscosity of the fluid	FT/L^2	M/LT
σ	Surface tension of fluid	F/L	M/T^2
g	Acceleration of gravity	L/T^2	L/T^2
C	Speed of sound in fluid	L/T	L/T
p	Pressure in fluid	F/L^2	M/T^2L

i.e. Reynolds Number and pipe roughness (or relative pipe roughness) are important dimensionless products in the analysis of pipe flow.

Click here for examples of forming dimensionless products using the method of

repeating variables. Click here for an example using the method of exponents.

Click here to continue with a discussion of similitude.

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