The stream function is given by the expression ψ = 2x² - y². What is the resultant velocity at a point denoted by x = 2 and y = 3 ?

Question

Question

This question was previously asked in

UPSC ESE Prelims (Civil) 20 Feb 2022 Official

Answer 1

Explanation:

Given;

Stream function

ψ = 2x² - y²

As per Cauchy Riemann equations

\(u = -\frac{\partial\psi}{\partial y}\) = - (-2y) = 2y

\(v = \frac{\partial\psi}{\partial x}= 4x\)

At (2,3),

u = 6 unit

v = 8 units

The resultant velocity is

(V) \(=\sqrt{u^2+v^2}\)

V \(=\sqrt{6^2+8^2}\)

V = 10 units

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