Page 75 - Mechanical Engineers' Handbook (Volume 4)

64 Fluid Mechanics

metrically similar systems exists when the appropriate dimensionless groups are the same
for the two systems. This is the basis on which model studies are made, and results measured
for one flow may be applied to similar flows.
The dimensions of some parameters used in fluid mechanics are listed in Table 5. The
mass–length–time (MLT) and the force–length–time (FLT) systems are related by F Ma
2
2
ML/T and M FT /L.
Force ratios are expressed as
2
Inertia force LV 2 LV
, the Reynolds number Re
Viscous force VL
2
Inertia force LV 2 V 2 V
or , the Froude number Fr
3
Gravity force Lg Lg Lg
Pressure force
pL 2
p
p
or , the pressure coefficient C
2
2
Inertia force LV 2 V 2 V /2 p
Table 5 Dimensions of Fluid and Flow Parameters
FLT MLT
Geometrical characteristics
Length (diameter, height, breadth,
chord, span, etc.) L L
Angle None None
Area L 2 L 2
Volume L 3 L 3
Fluid properties a
2
Mass FT /L M
Density ( ) FT /L 4 M/L 3
2
Specific weight ( ) F/L 3 M/L T 2
2
2
Kinematic viscosity (v) L /T L /T
2
Dynamic viscosity ( ) FT/L 2 M/LT
Elastic modulus (K) F/L 2 M/LT 2
Surface tension ( ) F/L M/T 2
Flow characteristics
Velocity (V) L/T L/T
Angular velocity ( ) 1/T 1/T
Acceleration (a) L/T 2 L/T 2
Pressure (
p) F/L 2 M/LT 2
Force (drag, lift, shear) F ML/T 2
Shear stress ( ) F/L 2 M/LT 2
Pressure gradient (
p/L) F/L 3 M/L T 2
2
3
3
Flow rate (Q) L /T L /T
˙
Mass flow rate (m) FT/L M/T
Work or energy FL ML /T 2
2
Work or energy per unit weight L L
Torque and moment FL ML /T 2
2
2
Work or energy per unit mass L /T 2 L /T 2
2
a
Density, viscosity, elastic modulus, and surface tension depend on temperature, and therefore temperature will not be
considered a property in the sense used here.