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 the 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:

To determine the degree of streamlining based on drag coefficient, remember that more streamlined shapes (such as tubes) have lower drag coefficients compared to blunt shapes (like square cylinders).

Answer 1

The Correct Option is A

In fluid dynamics, the drag coefficient \( C_d \) is a measure of the resistance experienced by an object as it moves through a fluid. The degree of streamlining of an object is directly related to its drag coefficient—streamlined objects tend to have lower drag coefficients. 
Let’s analyze each case step by step: 
1. \( P \) - Square Cylinder (Flow direction: right): 
The square cylinder has the highest drag coefficient among all the shapes, because the sharp corners and flat surfaces create significant resistance to the flow of fluid. Therefore, the drag coefficient for \( P \) is the highest, which is \( 2.1 \), and this shape is the least streamlined. 
2. \( Q \) - Square Cylinder (Flow direction: top-right): 
When the square cylinder faces the flow at an angle (like in \( Q \)), it still experiences a significant drag, but slightly less than the one facing directly. Hence, the drag coefficient for \( Q \) is \( 1.6 \). 
3. \( R \) - Half Tube (Flow direction: left): 
The half-tube shape is more streamlined than the square cylinders. The fluid flow around the half-tube is more continuous and experiences less resistance, making the drag coefficient lower. For \( R \), the drag coefficient is \( 1.2 \), which is the lowest among the shapes listed. 
4. \( S \) - Half Tube (Flow direction: right): 
The half-tube facing the flow from the right (as in \( S \)) has a drag coefficient of \( 2.3 \), which is still lower than the square cylinders but higher than the half-tube facing the flow from the left. Based on this analysis, the correct matching is: \[ P = 3 ({Square Cylinder with the highest drag coefficient}) \] \[ Q = 2 ({Square Cylinder with a slightly lower drag coefficient}) \] \[ R = 1 ({Half Tube with the lowest drag coefficient}) \] \[ S = 4 ({Half Tube facing the flow from the right}) \] Thus, the correct match between Group-I and Group-II is: \( P = 3, Q = 2, R = 1, S = 4 \).