Question

The left-hand column lists some non-dimensional numbers and the right-hand column lists some physical phenomena. Indicate the correct combination.

• A. 1-iii, 2-i, 3-ii, 4-iv
• B. 1-i, 2-ii, 3-iv, 4-iii
• C. 1-iv, 2-iii, 3-iv, 4-iii
• D. 2-iv, 1-iii, 3-ii, 4-i

Hint:

In fluid dynamics, the key non-dimensional numbers (Reynolds, Froude, Mach, and Weber numbers) are essential in understanding different flow behaviors, such as drag, wave effects, compressibility, and spray formation.

Answer 1

The Correct Option is A

In this problem, we need to match the non-dimensional numbers (on the left) with the corresponding physical phenomena (on the right). Let's break down the matching: 1. Reynolds number (Re):
- Reynolds number is a dimensionless quantity used to predict the flow regime in fluid dynamics, particularly whether the flow is laminar or turbulent.
- It is the ratio of inertial forces to viscous forces and is primarily related to viscous drag. In turbulent flow, viscous drag increases, and Reynolds number is used to characterize this.
- Therefore, Reynolds number matches with iii (Viscous drag).
2. Froude number (Fr):
- Froude number is used in fluid mechanics to describe the ratio of inertial forces to gravitational forces. It is particularly useful when analyzing free-surface flows, such as in open-channel flow or ship motion. - It is related to the formation of waves and the study of wave drag, especially in the context of open-channel or water flows.
- Therefore, Froude number matches with i (Wave drag). 3. Mach number (Ma):
- Mach number is a dimensionless quantity used in compressible fluid flow to quantify the speed of an object moving through a fluid compared to the speed of sound in that fluid.
- It helps us analyze compressible flow, where the speed of flow is comparable to the speed of sound, and shock waves may form.
- Therefore, Mach number matches with ii (Compressible flow).
4. Weber number (We):
- Weber number is a dimensionless number used in fluid dynamics to describe the relative importance of inertial forces to surface tension forces, commonly used in analyzing drop formation and spray dynamics.
- It plays a key role in spray formation, such as in atomization processes, where surface tension and inertial forces balance to form droplets.
- Therefore, Weber number matches with iv (Spray formation).
Thus, the correct combination is (A): 1-iii (Reynolds number - Viscous drag), 2-i (Froude number - Wave drag), 3-ii (Mach number - Compressible flow), and 4-iv (Weber number - Spray formation).