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# ps2 - 2.23 Hydrofoils Propellers Homework Assignment#2...

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2.23 Hydrofoils & Propellers Homework Assignment #2 Assigned: Fri. Feb. 23, 2007 Due: Fri. Mar 2, 2007 1) Perform a numerical integration on the following function I = 0 5 cos 2 ( x ) + 3 e x + x 3 dx From x=0 to x=5 Using: a) Trapeziodal rule with 100 steps b) Trapezoidal rule with 200 steps c) Above results + Richardson extrapolation equation (This is a 2 iteration Romberg integration) d) Using a 2 point Gaussian Quadrature method 2) Implement an Euler method solution in Matlab code to solve the differntial equation: di dt = 1.5 + 2.5 i a) Compute and plot the exact solution of the integral from time t=o to t=3. b) Implement a central difference Euler solution ti I as a function of time with intial conditions i=0 at t=0 up to a time of t=3. c) Run the euler solution for various stepsizes from 0.2 to .002 d) Produce a plot showing the exact solution and a few different stepsize solutions showing convergence with stepsize. 3) A propeller on a ship body has a diameter of 3 meters and has an engine capable of producing 10,000 kW . a) Plot the limiting top speed for this ship as a function of drag on the ship.

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• Spring '07
• PaulD.Sclavounos
• Euler solution ti, Euler method solution, vortex velocity result, Propellers Homework Assignment, unit strength vortex

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