Consider steady, laminar, fully developed flow between two parallel plates. Let the upper plate move in the x-direction with a constant speed U. Pressure gradient dp/dx is not negligible. The

governing equation can be simplified as: 0=-\frac{d p}{d x}+\frac{d}{d y}\left(\mu \frac{d u}{d y}\right) 1. Taking dp/dx as a constant, derive the analytical solution for this problem. 2. Solve the above differential equation using finite difference method (b= \begin{aligned} &0.1 m, V=0.008 m / s, \rho=1000 \mathrm{~kg} / \mathrm{m}^{3}, \mu=8.9 \times 10^{-4} \mathrm{~Pa} \cdot \mathrm{s}, d p / d x=\\ &0.001 \text { ). Please attach the Matlab code to the report. } \end{aligned} 3. Compare the numerical solution with the analytical solution in Step 1. 4. Using different values of dp/dx (reducing from 0.001 to -0.004) and repeat Step 3.