A potential (i.e. steady-state, incompressible, inviscid, irrotational) flow can be described by a stream function w(x,y)...
help 1. A 2D inviscid flow field is represented by the velocity potential function: ° = Ax + Bx2 – By2. Where A = 1m/s, B = 15-7, and the coordinates are measured in meters. The flow density is p = 1.2 kg/m3. (a) (2 points) Calculate the velocity field. (b) (2 points) Verify that the flow is irrotational. (c) (2 points) Verify that the flow is incompressible. (d) (2 points) Obtain the expression of stream function. (e) (2 points)...
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).
W The stream function « in a two-dimensional flow field is given as Q = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function 0(x, y) for this flow field with boundary condition Q = 0 at x = 2, y = 1.
can you solve the last question (e) Q1. Consider a steady, two-dimensional, incompressible flow field has the velocity potential a) b) c) 2 (x-7)(x+y) Determine the velocity components and verify that continuity is satisfied. [4 marks] Verify that the flow is irrotational. [2 marks] Determine the corresponding stream function. [4 marks) Now, consider a steady, two-dimensional, incompressible flow defined by velocity components u = ax + b&v=-ay + cx, where a, b and care constants. Neglect gravity. d) e) Show...
Now evaluate the mass and momentum into and out of the CV shown with 1.0s y Rs 1.5 at (2) Let p 1200 kg/m2, Uoo- 20 m/s and cylinder radius R 0.01 m 1 cm and Az 1 m Note: The flow does not cross streamlines, so there is no flow across the side boundaries. Exit (2) NO SCALE Variable u vs y at x2-0 Inlet (1) y- H1 and v 0 constant u Uo constant v0 A) Find mass...