Question

Consider the flow of a Newtonian fluid with the velocity field U-(-29) i + 02-r) j. Find the -x)j. Find the pressure field /tr, y) ir the pressure at point x-О.ye 0 is equal top.. Assume: The flow is two dimensional . The flow is incompressible . The flow is steady

Answer 1

"Navier - stokes x - and y - relations: P(u partial u/partial x + v partial u/partial y + w partial u/partial z) = -partial p/partial x + mu(partial^2 u/partial x^2 + partial^2 y/partial y^2 + partial^2 u/partial z^2) P[-2xy(-2y) + (y^2 - x^2)(-2x)] = -partial p/partial x + mu (0 + 0 + 0) or partial p/partial x = -2p(xy^2 + x^3) y - momentum relation p(u partial v/partial x + partial v/partial y + w partial v/partial z) = -partial p/partial y + mu (partial^2 v/partial x^2 + partial^2 v/partial y^2 + partial^2 v/partial z^2) or p[-2xy(-2x) + (y^2 - x^2) (2y)] = partial p/partial y + mu (-2 + 2 + 0) or partial p/partial y = -2p(x^2 y + y^3) The two gradients partial p/partial x and partial p/partial y may be integrated P = integral partial p/partial x dx