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#1 2007-02-09 09:36:02

feicobain
Member
Registered: 2007-02-09
Posts: 1

Trapezium Rule!!

In fluid mechanics the following integral equation indicates Displacement thickness

img47.gif

use Trapezium rule to evaluate the integral equation.
use 9 intervals,
interval=0.125,
initial value of y, y0=0.07,
ue=3,
u is a function of y and there are 10 values for u:9 intervals
u0=0.3
u1=0.7
u2=1.2
u3=1.7
u4=2.1
u5=2.5
u6=2.8
u7=3
u8=3
u9=3

I am so confused about this question.  PLEASE HELP!!

Last edited by feicobain (2007-02-09 09:37:48)

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#2 2007-02-10 12:10:17

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Trapezium Rule!!

First a link if reading helps a little.
http://www.mathsrevision.net/alevel/pages.php?page=44
Then I'll try, though I'm new to this.
Basically it is one-half twice the height times the widths.
Its basically width times height times 2 divided by 2.
To get the widths of .125 times 9, you use the eight inner heights (u1 to u8) and sum them up and double them.
Then you add the left and right end heights, so add u0 and u9 to the double sum of u1..u8.
Now you divide by two and multiply by 0.125 for the answer.


igloo myrtilles fourmis

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#3 2007-02-10 12:15:22

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Trapezium Rule!!

So when you get the 8 inner numbers doubled and totalled, that's 16 times the height or so.
Then you add the two ends, thats 18 times the height or so.
Now the width is 0.125 times nine, nine intervals, so that 1.125.
So 1.125 times 18 heights divided by 2 divided by 9 gives the answer.
That's why the formula uses the 0.125 and not 1.125, because they do the same thing, but
don't think it thru like I am telling you.


igloo myrtilles fourmis

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#4 2007-02-10 12:18:27

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Trapezium Rule!!

Also, is ue always 3, a constant, and is the 0.07 even needed for this,
what about zero to 0.07's area??  I gotta go to a dance, bye.


igloo myrtilles fourmis

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