Re: Detector mass questions

Yes, this might well be desirable. The overall surface to volume ratio even
goes down a bit (it is 3/r for a sphere and 2/r for your cylindrical
insertion with
height=r), because the volume is bigger. Even for equal volumes the
surface to
volume ratio only increases with your configuration by about 3%. The change
in the number of PMTs needed is then probably not an issue.

Hans Jostlein wrote:

> Hi, Jonathan,
>
> Ang Lee pointed out that the detector mass is not 200 ton, but quite a
> bit less.
>
> I have calculated the mass for a 6.8 m diameter sphere , filled with
> mineral oil, made of 1/4 inch steel.
> I get 147 (metric) ton total.
> Supports and electronics may pop this up to about 150 ton, but not
> much more.
>
> I think we need to be careful not to add safety factors at every stage.
> Things can get funky quickly!
>
> Hans
> ____________________________________________________________________________
> By the way,
>
> if the borehole cost dominates (as I suspect), it may be worth looking
> at slightly non-spherical shapes.
> I have done a paper exercise of adding a cylindrical section equal to
> one radius (3.4 m) to the vessel.
> As one might expect the mass goes up (from 147 ton to 256 ton),
> accompanied by a large gain in fiducial volume, from 24.5 m^3 to 55
> m^3, more than double.
> It may be worth running the light collection Monte Carlo for this shape.
> The gain ratio will be available at any diameter.
> We may be able to do a better experiment, reduce cost, or both
>
> Hans
>
> _________________________________________________________________________________
>
>
>
>
> Pi
>
>
>
> 3.141593
>
>
>
>
>
> diameter
>
>
>
> 6.8
>
>
>
> m
>
>
>
>
> Volume
>
>
>
> 164.6362
>
>
>
> m^3
>
>
>
>
> Density of oil
>
>
>
> 850
>
>
>
> kg/m^3
>
>
>
>
> Oil Mass
>
>
>
> 139940.8
>
>
>
> kg
>
>
>
> 139.9408
>
>
>
> ton
>
>
>
>
>
>
>
> Surface area
>
>
>
> 145.2672
>
>
>
> m^2
>
>
>
>
> Steel thickness
>
>
>
> 6.35E-03
>
>
>
> m
>
>
>
>
> Steel density
>
>
>
> 7850
>
>
>
> kg/m^3
>
>
>
>
> Steel volume
>
>
>
> 9.22E-01
>
>
>
> m^3
>
>
>
>
> Steel mass
>
>
>
> 7.24E+03
>
>
>
> kg
>
>
>
> 7.241209
>
>
>
> ton
>
>
>
>
>
>
>
> Fiducial volume diameter
>
>
>
> 3.5
>
>
>
> m
>
>
>
>
> Fiducial volume
>
>
>
> 22.4493
>
>
>
> m^3
>
>
>
>
>
>
>
>
>
> Total mass
>
>
>
> 1.47E+05
>
>
>
> kg
>
>
>
> 147.182
>
>
>
> ton
>
>
>
>
>
>
>
>
>
>
>
>
> Add cylinder of height one radius:
>
>
>
>
>
>
>
>
>
>
> Added height
>
>
>
> 3.4
>
>
>
> m
>
>
>
>
> Added volume
>
>
>
> 123.4772
>
>
>
> m^3
>
>
>
>
> Added mass
>
>
>
> 104955.6
>
>
>
> kg
>
>
>
>
> Added surface area
>
>
>
> 72.63362
>
>
>
> m^2
>
>
>
>
> Added steel volume
>
>
>
> 4.61E-01
>
>
>
> m^3
>
>
>
>
> Added steel mass
>
>
>
> 3.62E+03
>
>
>
> kg
>
>
>
>
>
>
>
>
>
> Total added mass
>
>
>
> 1.09E+05
>
>
>
> kg
>
>
>
> 108.5762
>
>
>
> ton
>
>
>
>
>
>
>
> Fiducial volume diameter
>
>
>
> 3.5
>
>
>
> m
>
>
>
>
> Added Fiducial volume
>
>
>
> 32.71183
>
>
>
> m^3
>
>
>
>
>
>
>
>
>
> Total new mass
>
>
>
> 2.56E+05
>
>
>
> kg
>
>
>
> 255.7582
>
>
>
> ton
>
>
>
>
>
>
>
> Total new fiducial volume
>
>
>
> 55.16113
>
>
>
> m^3
>
>
>
>

-- 
Byron Roe (byronroe@umich.edu)
Office: 355 W. Hall   (734)764-4441
Mailing Address:  Department of Physics, Randall Laboratory
University of Michigan, Ann Arbor, MI 48109