Question

Identify the type of flow from the time series plots of instantaneous fluid velocity (\( u \)) at a point.

A. \[ \begin{array}{l} I - \text{unsteady turbulent flow}; \\ II - \text{steady turbulent flow}; \\ III - \text{steady laminar flow}; \\ IV - \text{unsteady laminar flow}. \end{array} \]
B. \[ \begin{array}{l} I - \text{steady turbulent flow}; \\ II - \text{unsteady turbulent flow}; \\ III - \text{unsteady laminar flow}; \\ IV - \text{steady laminar flow}. \end{array} \]
C. \[ \begin{array}{l} I - \text{steady turbulent flow}; \\ II - \text{unsteady turbulent flow}; \\ III - \text{steady laminar flow}; \\ IV - \text{unsteady laminar flow}. \end{array} \]
D. \[ \begin{array}{l} I - \text{steady turbulent flow}; \\ II - \text{unsteady laminar flow}; \\ III - \text{unsteady turbulent flow}; \\ IV - \text{steady laminar flow}. \end{array} \]
 

Hint:

To classify flow types, observe the time series for velocity: 1. Fluctuations with a consistent mean indicate turbulence. 2. Periodicity or irregular variations indicate unsteadiness. 3. Constant values indicate steady laminar flow.

Answer 1

Step 1: Analyze the time series plots. 
1. Plot I: The velocity fluctuates irregularly but maintains a consistent mean. This indicates a steady turbulent flow, where turbulence exists but the overall flow is steady. 
2. Plot II: The velocity fluctuates irregularly and varies over time. This indicates an unsteady turbulent flow, where turbulence and unsteadiness are present. 
3. Plot III: The velocity is constant over time. This indicates a steady laminar flow, characterized by smooth and orderly motion. 
4. Plot IV: The velocity oscillates sinusoidally with time. This indicates an unsteady laminar flow, where the motion is smooth but varies periodically over time. 

Step 2: Match the plots to the flow types. 
Based on the analysis: I: Steady turbulent flow, II: Unsteady turbulent flow, III: Steady laminar flow, IV: Unsteady laminar flow. Conclusion: The correct identification is: \[ \text{I - steady turbulent flow; II - unsteady turbulent flow; III - steady laminar flow; IV - unsteady laminar flow}. \]