Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Dimensional analysis – concepts of geometric dimensionless numbers
Question Statement:
In fluid mechanics and open channel hydraulic modeling, which dimensionless number represents the ratio of inertial force to gravitational force, governing free-surface wave propagation and hydraulic jump phenomena?
Options:
(A) Froude number ($Fr = \frac{V}{\sqrt{g L}}$)
(B) Reynolds number ($Re = \frac{\rho V L}{\mu}$)
(C) Weber number ($We = \frac{\rho V^2 L}{\sigma}$)
(D) Euler number ($Eu = \frac{\Delta p}{\rho V^2}$)
Answer Key:
A
Step-by-Step Solution & Explanation
- Froude number ($Fr$) represents the square root of the ratio of inertia force to gravity force ($Fr = \frac{V}{\sqrt{g L}}$). It governs all open-channel, weir, and spillway hydraulic modeling.
- Reynolds number governs viscous dissipation.
- Weber number governs surface tension phenomena (droplet breakup, thin-film aeration).
- Euler number governs pressure-gradient driven flows. Option A is correct.