The theory of complex variable comes in naturally in the study of fluid phenomena.Let us define, w = φ + iψ with φ velocity potential and ψ stream function of a two dimensional fluid flow. w is called the complex potential function.Then w turns out to be analytic because the Cauchy-Riemann conditions, ∂φ/∂x =∂ψ/∂y ; ∂φ/∂y = −∂ψ/∂x are exactly the natural flow conditions that have to be satisfied. Suppose, velocity potential for a two dimensional fluid flow is given by the function φ(x, y) = y/x2+ y2− 2xy.Find out the stream function. Also find the complex potential function for the fluid flow.
The theory of complex variable comes in naturally in the study of fluid phenomena.Let us define, w = φ + iψ with φ velocity potential and ψ stream function of a two dimensional fluid flow. w is called the complex potential function.Then w turns out to be analytic because the Cauchy-Riemann conditions, ∂φ/∂x =∂ψ/∂y ; ∂φ/∂y = −∂ψ/∂x are exactly the natural flow conditions that have to be satisfied. Suppose, velocity potential for a two dimensional fluid flow is given by the function φ(x, y) = y/x2+ y2− 2xy.Find out the stream function. Also find the complex potential function for the fluid flow.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The theory of complex variable comes in naturally in the study of fluid phenomena.Let
us define,
w = φ + iψ
with φ velocity potential and ψ stream function of a two dimensional fluid flow. w is called the complex potential function.Then w turns out to be analytic because the Cauchy-Riemann conditions,
∂φ/∂x =∂ψ/∂y ; ∂φ/∂y = −∂ψ/∂x
are exactly the natural flow conditions that have to be satisfied.
Suppose, velocity potential for a two dimensional fluid flow is given by the function
φ(x, y) = y/x2+ y2− 2xy.Find out the stream function. Also find the complex potential function for the fluid flow.
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