ES100: Homework 4 (25 points) Introduction to Engineering Use of Computers Spring 2019 Homework Requirements (Gpts) 1. File Name Format: Lastname .HW. #ES100XXS19.En (where s the HW, mumber and XX is your section number). 2 Heading Format: Include your Full Nanae, HW-H, ES 100XX S19, and Due Date each in a separate line. 3. Commenting: Thoroughly comment your code including units throaghout the code and on all answers (if Run-Time Errors: Program should run without any run-time errors (red text in command window). . Solution Variables Names: All solution variables should be named exactly as speciied in the problem state- ments. Variables names are given in bold text Problem 1 (10 pts) The Navier-Stokes Equation can be used to find an exact solution for fluid flow over an oscillating plate. The oscillation of the plate below is described by the function Uwhere Uo is the amplitude, w is the frequency, and t is time. Viscous Fluid U, coset The exact solution for the the fluid velocity above the oscillating plate is given by the following equation: where u is the fluid velocity, y is the vertical distance from the oscillating plate, r and is the kinematic viscosity of the fluid. Assume the fluid is water, which has a kinematic viscosity of 0.01 ms. Assume an amplitude of 100 cm/s and a frequency of rad/s Evaluate the following for times 0-10 s (every second). a) Find the fluid velocity at a height of 0.5 em from the oscillating plate. The final answer will be in units of cm/s. Label the final answer ua. b) Find the uid velocity at a height of 1 em from the oscillating plate. Label the final answer ub e) As vertical distance from the plate increases, does the magnitude of the fluid velocity increase or de- crease? Write your answer as a comment in your code