ME218 hw8_2011 - Problem 3 Initial Value Problem(1 st order...

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ME 218: ENGINEERING COMPUTATIONAL METHODS Home Work #8 Assigned: October 28, 2011 Due: November 3, 2011 Name: __________________UT EID: ____________Unique: _________ Lab Time: (Mon/Tue) ___PM Problem 1: Numerical Integration (Trapezoidal formula) Motor is pulling a mass over a period of 2.5 seconds. Motor forces and velocities of the mass are sampled every 0.5 seconds and are listed in the table below. Evaluate total work performed by this motor. t (seconds) 0 0.5 1.0 1.5 2.0 2.5 Force (N) 1.9 1.6 1.7 2.1 0.8 0.4 Velocity (m/s) 0.1 0.5 0.9 1.5 1.9 2.2 Problem 3: Initial Value Problem (1 st order ODE - Euler’s Method) Solve the following differential equation using Euler’s method, assuming that at x = 0, y = 7. Integrate to x = 2 with a step size of 0.5. dy/dx = -0.8 y 2 Solve this problem by hand, without using the help of any computer application. Report all intermediate steps and finally, tabulate the values of y Problem 3 is on the next page!!!
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Unformatted text preview: Problem 3: Initial Value Problem (1 st order ODE - Euler’s Method) A spherical tank has a circular orifice in its bottom through which the liquid flows out as shown in the figure. The outflow rate Q through the 3 cm-dia. hole can be estimated as: dt dV gH CA Q tank − = = 2 (Equation A) where C =0.55, A = ] [ ) 2 / 03 . ( 2 2 m × π , g= ] / [ 8 . 9 2 s m , and the liquid volume in a partially filled spherical tank is given as: ) 3 ( 3 2 H r H V − = . (Equation B) The tank’s diameter (2r) is 3m and the initial height (H) of the water surface is 2.75m. Using Euler’s method with a uniform step of Δ t = 0.5 seconds, determine how long it will take to drain out the liquid in the tank. Write a Matlab program to solve this problem. But do not use any built-in ODE solver in Matlab! Hint: Substitute the formula for V in Equation B into Equation A to obtain a differential equation in height (H)....
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This note was uploaded on 12/14/2011 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas.

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ME218 hw8_2011 - Problem 3 Initial Value Problem(1 st order...

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