-
The flow of glycerin (kinematic viscosity, v = 5 × 10-4 m2 /s) in an open channel is to be modeled in a laboratory flume using water (v = 10-6 m2 /s) as the flowing fluid. If both gravity and viscosity are important, what should be the length scale (i.e. ratio of prototype to model dimensions) for maintaining dynamic similarity?
-
- 1
- 22
- 63
- 500
- 1
Correct Option: C
| Viscous force → Reynold’s number |  |  | ||
| μ |
| Gravity force → Froude’s number | | | ||
| √gy |
Here, ‘d’ and ‘y’ are same as viscosity and gravity are equally important.
| = | = | ||||
| μ | v | v |
| = | ||||
| vr | √Lr |
(Lr)3 / 2 = vr
| L = (vr)2 / 3 = | | | 2 / 3 | ||
| vo |
| = | | | 2 / 3 | ||
| vo |
| = | | | 2 / 3 | = 0.0158 | |
| 5 × 10-4 |
| Lr = | ||
| Lp |
| ∴ | = | = | ≈ 63 | |||
| Lm | Lr | 0.0158 |
