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MathGroup Archive 2006

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Beginner--Beginner: Calculating Ave Intensity in a domain of n points

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68776] Beginner--Beginner: Calculating Ave Intensity in a domain of n points
  • From: madhukarrapaka at yahoo.com
  • Date: Fri, 18 Aug 2006 03:12:32 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi All 
I am a stranger to mathematica. I would like to calculate the average intensity in a UV reactor. (The reactor is a cylinder with a UV lamp placed parallel to the height of the cylinder.) 

cylinder dimensions(say)base=40 mm, height=600mm; 
length of UV lamp=450mm).
The Intensity at a point due to the UV lamp is given by:I= P/(2*pi*r*L). 
where r=distance of the pt. from the centre of the lamp; 

        pi=3.14;
        L= lamp length
        P=power of the lamp.
If i want to calculate the Ave. Intensity in the reactor, how to program this in Mathematica. 
Ave. Intensity I_ave=Summation(I) over all the points of the volume. 

Please give me a hint how to write a program for this in Mathematica. 

Here i am giving my procedure, which doesn't give desired result
       
x = 0; y = 0;(x,y) is the coordinates of the lamp centre. 

 P = 10.3; Power of the lamp .
l = 0.45; Length of the lamp.
 r0 = 0.025; Radius of the lamp.
 r[xk_, yk_] := Sqrt[(x - xk)^2 + (y - yk)^2]; distances from the centre of the lamp to Kth point in the domain. 

Intensity[xk_, yk_] := (P/(2*\[Pi]*(Sqrt[(x - xk)^2 + (y - yk)^2])*l)); 

Integrate[Intensity[xk, yk], {xk, -0.1, 0.1}, {yk, 0, 0.2}] 

Actually i need to calculate the ave. intensity in a volume V of a Reactor. For this i have to find the Intensity at a point P(Xk,Yk), which is at a dist. of 'r' from the centre of the lamp ie (0,0). 

Please anyone tell me how to do this and how to plot the Intensity field. 

Thanks in Advance 


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