3. Course: Mech. Engg.
Subject: Fluid Mechanics
Chapter: Dimensional Analysis
Some topics:
*Dynamic Similarities
*Various model laws:
Reynolds model law
Froude’s model law
Euler’s model law etc.
Such as:
Point of Focus
4. Reynold’s Model Law:
Whenever viscous forces predominate over inertia or other forces for dynamic
similarity, the Reynold’s number for the model must be equal to the Reynold’s number
for the prototype. i.e. (Re)model = (Re)prototype
Used for:
(i) Flow in closed pipes, flow meter, fans etc.
(ii) Flow around immersed bodies like aero plane, submarine etc.
6. In order to examine flow conditions:
•For pipe, Lc is inner diameter of pipe.
•For square duct, Lc is side of cross-section.
• For airfoil, Lc is chord length.
7. If the temperature and pressure of the air used for testing model and prototype are
same then, the value of the kinematic viscosities of both will also the same.
8. * ______ = ______ * _______
10m/s 5m
1m
50m/s
• If Scale= 1:5
•Wind velocity required in wind tunnel is 5x
•Thus more we scale down our model more wind
velocity requires.
•This means that size of the fan required
is large.
•Consequently the size of the wind tunnel
comes out to be very large.
9. To maintain the different temperature and pressure as compared to
atmosphere Closed Circuit Wind Tunnel comes into picture
Kinematic Viscosity (ν) = µ/ρ
As Temperature ↓ Kinematic Viscosity ↓
Also Pressure↑ Kinematic viscosity ↓
* ______ = ______ * _______
10m/s 5m
1m
ν/2 ν
25m/s
If the νmodel ≠ νprototype
Extra point:
10. Conclusion
•Reynolds model law must be followed
•Due to scaling the velocity of the air in the wind tunnel requires at high
speed for that purpose the size of wind tunnel comes out be large.
