Question

Problem
• A stream function is given by: Y= 5x-6y.
Calculate the velocity components and also
magnitude and direction of the resultant
velocity at any point.
OP
U =-
бр
oy
V=
ox
u= 6; v = 5
Magnitude = (6^2 + 5^2)^0.5
Direction= tan-1(v/u)​

Answer 1

Answer:

● Problem 5.12 A stream function is given by y = 5x - 6y . Calculate the Velocity Components and also Magnitude and Direction of the Resultant Velocity at any Point ●.

☆ Solution :- y = 5x - 6y ☆.

Explanation:

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Answer 2

Answer:

The resultant velocity is 7.81m/s and

The direction of resultant velocity is 39.79°

Explanation:

The proper question is

"A stream function is given by: Y= 5x-6y.

A stream function is given by: Y= 5x-6y.Calculate the velocity components and also magnitude and direction of the resultant velocity at any point."

Given that,The stream function is

$Ψ = 5x - 6y$

We know that the components of stream.function and velocity are related as follows

$u = - \frac{dΨ}{dy} \\ v = \frac{dΨ}{dx}$

Hence,substituting the given stream function the above two relations,we get

$u = \frac{ - d}{dy} (5x - 6y) = 6 \\ v = \frac{d}{dx} (5x - 6y) = 5$

The components of velocity are known.We know that velocity is written as

$V=ui+vj$

Magnitude of velocity is given as

$|V | = \sqrt{u {}^{2} +v {}^{2} } \\ = > |V | = \sqrt{6 {}^{2} + 5 {}^{2} } = 7.81ms {}^{ - 1}$

Direction of velocity at any point is given by relation

$\alpha = tan {}^{ - 1} ( \frac{v}{u} )$

Substituting the known values we get

$\alpha = tan {}^{ - 1} ( \frac{5}{6} ) = 39.79 {}^{0}$

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