Question #149106

If for a two dimensional potential flow, the velocity potential is given by : φ = 4x(3y - 4), determine the velocity at the point (2, 3). Determine also the value of stream function ψ at the point (2, 3).

Expert's answer

In velocity we can write

Given "\\varphi=4x(3y-4)"

"u=\\dfrac{\\partial\\varphi}{\\partial x}=12y-16, v=\\dfrac{\\partial\\varphi}{\\partial y}=12x"Calculate the velocity at the point (2, 3)

"|velocity|=\\sqrt{u^2+v^2 }=\\sqrt{(20)^2+(24)^2}=4\\sqrt{61}"

"u=\\dfrac{\\partial\\psi}{\\partial y}, v=-\\dfrac{\\partial\\psi}{\\partial x}"

"u=\\dfrac{\\partial\\psi}{\\partial y}=12y-16"

Integrate with respect to "y"

"-\\frac{\\partial\\psi}{\\partial x}=-\\frac{dg}{d x}=12x"

Integrate with respect to "x"

Then

Learn more about our help with Assignments: Vector Calculus

## Comments

## Leave a comment