Question

The mathematical form of the stream-function for 2-D SSSF satisfies the Laplace Equation inside a 2-D region in space (or inside a control volume) with specific boundary conditions on the entire control surface enclosing the region, The values for the velocity components at any given point in the flow field are determined from:

A. The velocity components at arty point are found by solving the clinical Armour, equation
B. The velocity components at any pant are found by integrating the stream function around the boundary (control surface)
C. The velocity components at any pant are found by integrating the stream functran over the entire flow field region (control volume)
D The velocity components at any point are found from the first partial derivatives of the stream function at the given point

Answer 1

D. The velocity components at any point are found from the first partial derivatives of the stream function at the given point

Step-by-step explanation:

The stream function can be used to plot the streamlines of the flow and find the velocity. For two-dimensional flow the velocity components can be calculated in Cartesian coordinates by u = −∂ψ/∂y and v = ∂ψ/∂x,

where u and v are the velocity vectors (components) in the x and y directions, respectively, ψ is the stream function.

From the above, the velocity components at any point are found from the first partial derivatives of the stream function at the given point.