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

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

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.

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

Hi,
you want to calculate the mean value of a function: fun in a cylindrical
region. You can do this by calculating the integral of the function over
the region and divide by the volume. In your case this is best done ijn
cylindrical coordinates. Here, the volume element is:
r dphi dr dz
where r is the distance from the axis, z the heigth and phi the angle.
As the function fun only depends on r an z the angular integral can be
done at once, giving 2 Pi. This leaves:
2 Pi NIntegrate[r fun[r,z],{r,rmin,rmax},{z,0,zmax}] /
((rmax^2-rmin^2)Pi zmaz)

Daniel