Question

A doublet is the resulting flow pattern when a sink and a source of equal strength are brought together. Which one of the following options correctly represents the nature of the product of the strength and the distance between them during approach?

• A. Remains always constant
• B. Continuously decreases
• C. Continuously increases
• D. First increases and then continuously decreases after reaching a maximum

Hint:

A doublet is mathematically the limit of a source–sink pair as separation $\to 0$ while $q \cdot d$ remains constant. This is a fundamental concept in potential flow theory.

Answer 1

The Correct Option is A

Step 1: Recall definition of doublet.
A doublet is formed by combining a source and a sink of equal strength $q$ at a very small separation distance $d$, while keeping the product $q \cdot d$ finite.

Step 2: Strength–distance product.
The parameter of a doublet is defined as: \[ \mu = q \cdot d. \] This parameter $\mu$ is what characterizes the doublet potential and velocity field.

Step 3: During approach of source and sink.
As the source and sink approach each other ($d \to 0$), their individual strengths remain fixed, and the definition of a doublet is such that the product $q d$ stays constant.

Step 4: Conclusion.
Hence the product of strength and distance between them remains constant during the approach. Final Answer:
\[ \boxed{\text{Remains always constant}} \]