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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.
- Fall '08