Question

Group-I shows different two-dimensional bodies and Group-II mentions their total drag coefficient $(C_D)$ based on frontal area while facing parallel flow of fluid having Reynolds number $Re \geq 10^4$ along the direction of arrow. The bodies are placed symmetrically with respect to the flow direction.

Which one of the following options identifies the correct match between Group-I and Group-II, as per the concept of degree of streamlining?

• A. P–3, Q–2, R–1, S–4
• B. P–3, Q–2, R–4, S–1
• C. P–2, Q–3, R–1, S–4
• D. P–3, Q–1, R–2, S–4

Hint:

Bluff bodies (flat faces to flow) have higher $C_D$, while streamlined shapes (diamond orientation, convex side leading) have lower $C_D$. Always rank drag coefficients by degree of streamlining.

Answer 1

The Correct Option is A

Step 1: Concept of drag coefficient ($C_D$).
The drag coefficient depends strongly on the degree of streamlining: - Bodies with blunter shapes (like flat square cylinders or half tubes with flat side facing flow) produce higher drag. - More streamlined bodies (diamond-shaped orientation or curved convex sides facing flow) have lower drag coefficients.

Step 2: Expected values.
From experimental data for 2D bluff bodies at high $Re$: - Flat square cylinder ($P$) → high drag $\approx 2.1$. - Square cylinder at $45^\circ$ (diamond, $Q$) → drag reduced $\approx 1.6$. - Half tube with convex side facing flow ($R$) → streamlined, drag $\approx 1.2$. - Half tube with flat side facing flow ($S$) → least streamlined, highest drag $\approx 2.3$.

Step 3: Match with Group-II.
- $P \rightarrow 3 \; (2.1)$ - $Q \rightarrow 2 \; (1.6)$ - $R \rightarrow 1 \; (1.2)$ - $S \rightarrow 4 \; (2.3)$

Step 4: Verify options.
Only option (A) matches this sequence. Final Answer:
\[ \boxed{\text{P–3, Q–2, R–1, S–4}} \]