Dimensions and Units used in Fluid Mechanics

Key Concept: Dimensions refer to mass, force, length, and time irrespective of the units

used such as slugs/kg, lb,/Newtons, feet/meters, seconds.

In a Nutshell: Of the four basic dimensions in fluid mechanics force, mass, length, and
time, any three are independent. The fourth one is derived. The two most common sets of dimensions are the FLT system and the MLT system. The table below lists the dimensions for physical quantities in fluid mechanics.

Physical Quantity FLT System MLT System

Density	FT^2/L^4	M/L^3
Shear Stress	F/L^2	M/LT^2
Pressure	F/L^2	M/LT^2
Specific Weight	F/L^3	M/L^2T^2
Dynamic Viscosity Kinematic Viscosity	FT/L^2 L^2/T	M/LT L^2/T

The British Gravitational System (BG) and the International System (SI) are used

in the study of fluid mechanics. The table below lists common units used.

BG	lb	slugs	ft	sec	^oF or ^oR
SI	N(newtons)	kg	m (meters)	sec	^oC or ^oK

Length: 1 inch = 2.54 cm, 1 ft = 0.3048 m Pressure: 1 lb/in² = 6.894 N/mm²

Energy: 1 Joule = 1 N m Force: 1 N = 1 kg m / sec²

Gravitational Constant: 1 g = 32.174 ft/sec² 1 g = 9.807 m/sec²

^oF = (9/5)^oC + 32, ^oC = (5/9)(^oF – 32), Absolute temps ^oR = ^oF + 460,

Absolute temps ^oK = ^oC + 273 Also note: 1 N/mm² = 1 mPa

Click here to continue with discussion of dimensional homogeneity.

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