Given the following expression for the pressure field where

Question

1. Using the expression for the gradient in polar coordinates (Appendix A), find the gradient of ψ(r,θ) when

Where is the gradient maximum? The terms A and a are constant.

2. Given the following expression for the pressure field where x, y, and z are space coordinates, t is time, and P₀, ρ, V∞, and L are constants, find the pressure gradient