PROBLEM 7.2
Streamline y = constant
Equipotential line = constant
The two-dimensional flow of a nonviscous, incompressible fluid in the vicinity of a corner (see figure) is described by the following potential flow: Φ = 2Vrcos^2θ, where r is in meters, V = 10 m/s, and assume the fluid is air with Ï = 1.225 kg/m^3.
1. Show that the velocity for this potential flow is:
u = 4Vrcosθ, g = -4Vrsinθ
Hint:
∂Φ/∂r = u = 4Vrcosθ
∂Φ/∂θ = g = -4Vrsinθ
2. Determine the stagnation point in the flow, if any.
Hint: V = 0
3. Show if the flow is a physically possible incompressible flow.
Hint: find where ∂V/∂θ = 0
4. Determine the stream functions.
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