Question
Download Solution PDFDimension of circulation is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Circulation
- Circulation is a concept in fluid dynamics that measures the total "rotational effect" of a fluid flow around a closed contour or loop. It is mathematically defined as the line integral of the velocity vector along a closed curve. The dimension of circulation can be derived from its physical definition and mathematical representation.
Circulation is defined as the line integral of velocity over a closed loop:
\( \Gamma = \oint \vec{V} \cdot d\vec{l} \)
Where:
- \( \vec{V} \) = velocity (dimension = \( \frac{L}{T} \))
- \( d\vec{l} \) = length element (dimension = \( L \))
Therefore,
\( \text{Dimension of } \Gamma = \frac{L}{T} \times L = \frac{L^2}{T} \)
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