Question
Download Solution PDFWhich of the following related fluid flow parameters exist both in rotational and irrotational flows?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Velocity potential function:
\(u = - \frac{{\partial \phi }}{{\partial x}};\;v = - \frac{{\partial \phi }}{{\partial y}}\)
(i) If velocity potential (ϕ) exists, the flow should be irrotational.
(ii) If velocity potential (ϕ) satisfies the Laplace equation, it represents the possible steady incompressible irrotational flow.
Stream function:
\(u = - \frac{{\partial \psi }}{{\partial y}};\;v = \frac{{\partial \psi }}{{\partial x}}\)
(i) If stream function (ψ) exists, the flow may be rotational or irrotational.
(ii) If stream function (ψ) satisfies the Laplace equation, it represents the irrotational flow.
Vorticity:
Defined as the value twice of the rotation
\(\zeta = 2\omega \)
For an irrotational flow, vorticity components are zero
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