Question

Problem 2 Consider an incompressible fluid flow field ⃗(x, y) = (, ) = (10x + 2) ⃗ + (−10y − 4) ⃗ and P (x=2, y=1) = 1. The fluid density is r, a constant. (a) Calculate vorticity of this flow field. Is this flow rotational? (b) calculate the shear strain rate of the flow field. (c) calculate the volumetric strain rate. (d) calculate the materials derivative of the flow field. (e) obtain numerical value of flow acceleration at (x=2, y=1). (f) Obtain the analytical expression for the streamlines, (g) plots several (3 or more) streamlines with vectors superimposed to indicate the flow direction). (h) Using the Bernoulli equation to calculate the numerical value of the pressure at another point (of your choice) on the streamline that passes through point (x=2, y=1).

Answer 1

In this physics problem, we analyze an incompressible fluid flow field and determine various properties such as vorticity, shear strain rate, volumetric strain rate, flow acceleration, and pressure using mathematical calculations and equations.

(a) To calculate the vorticity of the flow field, we need to take the curl of the velocity vector. Given the velocity field