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. \[ \begin{array}{l} I - \text{steady turbulent flow}; \\ II - \text{unsteady laminar flow}; \\ III - \text{unsteady turbulent flow}; \\ IV - \text{steady laminar flow}. \end{array} \]
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. \[ \begin{array}{l} I - \text{steady turbulent flow}; \\ II - \text{unsteady laminar flow}; \\ III - \text{unsteady turbulent flow}; \\ IV - \text{steady laminar flow}. \end{array} \]
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Solution and Explanation
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: \[ \text{I - steady turbulent flow; II - unsteady turbulent flow; III - steady laminar flow; IV - unsteady laminar flow}. \]
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