1. Reynolds
( )
Ernst Mach
(1838 – 1916)

2. SIGNIFICANT DIMENSIONLESS GROUPS
IN FLUID MECHANICS
Inertia
Viscous
Pressure
FORCES:
(in Fluid Mechanics)
Gravity
Surface Tension
Compressibility

3. PHYSICAL MEANINGS OF DIMENSIONLESS GROUPS DIMENSIONLESS GRUOPS Inertia
Reynolds Number
(Re)
Viscous
Euler Number
(Eu = Cp)
Pressure
DIMENSIONLESS
GRUOPS
Froude Number
(Fr)
Weber Number
(We)
Mach Number
(M)
Gravity
Surface Tension
Compressibility

4. FLOW SIMILARITY AND MODEL STUDY
EXPERIMENTAL DATA
To calculate
secondary data:
Must be Scaled
- Forces
- Moments, etc.
There must be similarity between MODEL and PROTOTYPE
- Similar in shape
- Constant (linear) scales
- GEOMETRIC SIMILARITY:
- KINEMATIC SIMILARITY:
- DYNAMIC SIMILARITY:
- Similar flow kinematics
- Constant scales (in magnitudes)
- All forces scaled constantly
- Needs geometric & kinematic sim’s.

5. FLOW SIMILARITY AND MODEL STUDY (Cont’d)
For complete analysis
All contributing forces must be presented:
- Viscous force
- Pressure force
- Surface tension force
- etc.
Buckingham p – theorem can be used

6. Drag force analysis on a sphere: F = f (D, V, r, m)
EXAMPLE
Drag force analysis on a sphere:
F = f (D, V, r, m) F
r, m, V D
From p – theorem, we have:
The flow will dynamically similar if:
Also:
Similarity in the ratio of drag to inertia forces between model & prototype
Similarity in the ratio of inertia to viscous forces between model & prototype

7. Sonar transducer model tested in a wind tunnel
EXAMPLE PROBLEM 7.4
Given:
Sonar transducer model tested in a wind tunnel
Find:
a) Vm
b) Fp
Solution:
The test should be run at:

8. EXAMPLE PROBLEM 7.4 5.02 x 105 Therefore: 5.02 x 105 And:
Vm = 156 ft/sec  m/s
Finally:
Fp = 54.6 lbf