Physics, asked by rosemarynjobvu2002, 5 months ago

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)​

Answers

Answered by dineshwari8
2

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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Answered by rinayjainsl
0

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}

#SPJ3

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