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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