Question

Among the following steps in the correct sequence for determining the flow regime and pressure drop of Newtonian fluids flowing through a pipe:
A. Calculate the Reynolds number to classify flow as laminar or turbulent
B. Use the Hagen–Poiseuille equation for laminar flow or friction factor charts for turbulent flow to find pressure drop
C. Measure or estimate fluid properties (density, viscosity), pipe diameter, and average velocity
D. Determine flow rate from velocity and cross-sectional area, relating to pressure drop via momentum balance
E. Identify critical Reynolds number transitions (Re $<$ 2100 laminar, Re $>$ 4000 turbulent)
Choose the correct answer from the options given below:

• A. A, C, E, B, D
• B. C, A, D, E, B
• C. C, A, E, B, D
• D. C, A, B, D, E

Hint:

Always calculate Reynolds number before selecting equations.

Answer 1

The Correct Option is C

Concept: Determination of flow regime and pressure drop in pipe flow involves systematic evaluation of fluid properties, Reynolds number, and appropriate equations.

Step 1: Measurement of properties (C).
First, we must determine:
• Density ($\rho$)
• Viscosity ($\mu$)
• Pipe diameter ($D$)
• Velocity ($v$) These are essential inputs for further calculations.

Step 2: Calculation of Reynolds number (A).
Using: \[ Re = \frac{\rho v D}{\mu} \] This helps classify flow.

Step 3: Identification of flow regime (E).
Based on Reynolds number:
• $Re < 2100$ → Laminar flow
• $Re > 4000$ → Turbulent flow

Step 4: Application of appropriate equation (B).

• Laminar → Hagen–Poiseuille equation
• Turbulent → Friction factor charts (Moody chart)

Step 5: Determination of flow characteristics (D).
Finally:
• Flow rate and pressure drop relationships are evaluated

Step 6: Final sequence. \[ C \rightarrow A \rightarrow E \rightarrow B \rightarrow D \] Final Conclusion:
Option (3) is correct.