Question

Match List-I with List-II

List-I (Dimensionless Numbers)	List-II (Relationship)
(A) Froude's Number	(II) \( \sqrt{\frac{\text{Inertia force}}{\text{Gravity force}}} \)
(B) Mach's Number	(IV) \( \sqrt{\frac{\text{Inertia force}}{\text{Elastic Force}}} \)
(C) Euler's Number	(I) \( \frac{\text{Pressure Force}}{\text{Inertia Force}} \)
(D) Weber's Number	(III) \( \frac{\text{Inertia Force}}{\text{Surface Tension Force}} \)

Choose the correct answer from the options given below:

• (A) (1), (B) (II), (C) (III), (D) (IV)
• (A) (I), (B) (III), (C) (II), (D) (IV)
• (A) (II), (B) (IV), (C) (1), (D) (III)
• (A) (III), (B) (IV), (C) (I), (D) (II)

Hint:

The dimensionless numbers help in analyzing fluid dynamics and each number represents a different physical relationship in the flow.

Answer 1

The Correct Option is B

Step 1: Match the dimensionless numbers with the correct relationships.
- Froude's number: \( \frac{\text{Inertia force}}{\text{Gravity force}} \) → (II)
- Mach's number: \( \frac{\text{Inertia force}}{\text{Elastic Force}} \) → (IV)
- Euler's number: \( \frac{\text{Pressure force}}{\text{Inertia force}} \) → (I)
- Weber's number: \( \frac{\text{Inertia force}}{\text{Surface Tension force}} \) → (III)
Final Answer: \[ \boxed{(A) (I), (B) (III), (C) (II), (D) (IV)} \]