Consider fully developed laminar flow in a circular pipe of a fixed le...
Understanding Fully Developed Laminar Flow in a Circular Pipe
In a circular pipe under fully developed laminar flow, the following concepts are fundamental:
1. Friction Factor and Reynolds Number
- The friction factor (f) is inversely proportional to the Reynolds number (Re) for laminar flow.
- This means as the Reynolds number increases, the friction factor decreases. For laminar flow, f = 64/Re.
2. Pressure Drop and Average Velocity
- The pressure drop (ΔP) in the pipe is directly proportional to the average velocity (V) of the flow.
- This is expressed as ΔP = f * (L/D) * (ρV²/2), where L is the length, D is the diameter, and ρ is the fluid density. In laminar flow, this relation holds true, making this statement correct.
3. Friction Factor for Rough vs. Smooth Pipes
- In laminar flow, the friction factor does not depend on the surface roughness of the pipe. The friction factor is determined solely by the Reynolds number.
- Thus, the statement that the friction factor is higher for a rough pipe compared to a smooth pipe is incorrect for laminar flow.
4. Pressure Drop and Average Velocity Squared
- The statement that pressure drop is proportional to the square of the average velocity is true in turbulent flow, not laminar flow.
- In laminar flow, it is proportional to the average velocity, not its square.
Conclusion
Therefore, the correct statements are:
- Statement 1 (Correct)
- Statement 2 (Correct)
- Statement 3 (Incorrect)
- Statement 4 (Incorrect)
Thus, the correct answer is option 'D' (1 and 2).
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