Question

6.35 The x component of velocity in a two-dimensional incompressible flow field is given by uAx; the coordi nates are measured in meters and A 3.28 m There is no velocity component or variation in the z direction. Calculate the acceleration of a fluid particle at poin (x, y)- (0.3, 0.6). Estimate the radius of curvature of the streamline passing through this point. Plot the streamline and show both the velocity vector and the acceleration vector on the plot. (Assume the simplest form of the y component of velocity.)

Answer 1

a) Given. u = Ax^2 A = 3.28 m^- 1. 3^- 1 Two dimensional Incompressible Flow. b) To Find. Acceleration of third at point (x, y) = (0.3, 0.6) Assumptions. * steady stake condition. * 2 - D How field problem * simplest Form of y component velocity - 1/2 A y^2. Governing equations. * continuity equation: partial differential p/partial differential t + partial differential pu/partial differential x + partial differential pv/partial differential y + partial differential pw/partial differential z = 0. Incompressible 2 - D continuity equation partial differential u/partial differential x + partial differential v/partial differential y = 0. * Acceleration a = Dv/Dt = partial differential v/partial differential t + partial differential v/partial differential x + v partial differential v/partial differential y + w partial differential v/partial differential z. 2 - D problem. ax = Du/Dt = partial differential u/partial differential t + u partial differential u/partial differential x + v