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.