forget to take - sign in option (Question:432700.0)

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zaved alam

· started a discussion

· 1 Months ago

forget to take - sign in option (Question:432700.0)

please correct options

Question:

A stream function is given by (x² - y²).

The potential function of the flow will be

Options:

2xy + f(x)

2xy + constant

2(x² - y²)

2xy + f(y)

Solution:

Ans: (b)

$\frac{d Ψ}{d x} = 2 x = \frac{d ϕ}{d y} ∴ \frac{d ϕ}{d y} = - 2 x$

And $\frac{d Ψ}{d y} = - 2 y = \frac{d ϕ}{d x} ∴ \frac{d ϕ}{d x} = - 2 y$

Now, $\frac{d ϕ}{d y} = - 2 x$

$∴ ϕ = - 2 x y + f (x)$

differentiating w. r. to x

$\frac{d ϕ}{d x} = - 2 y + f^{'} (x) = - 2 y$

$∴ f ’ (x) = O$

∴ f(x) = constant

∴ ϕ = - 2xy + constant

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forget to take - sign in option (Question:432700.0)

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