On Jul 26, 2009, at 4:03 PM, Frank wrote:
OK,
I follow your math now and it seems like a sound theory with the
only assumption that an inertial mass change occurs.
Regards
Francis X roarty
I'm glad you understand the calculation. Unfortunately, it has some
errors, and it is for much too large cells to produce much Casimir
effect. The scale needs to be more on the scale of 10-7 m to have an
effect. Here is a re-do of the calculation with approximate flow and
pressure information:
Input pressure: 100 atm
Flow velocity: 0.0001 m/s
Equivalent pipe diameter: 1E-7 m
Path length: 1 m length
Density of argon at 100 atm: 0.167 kg/l = 167 kg/m^3
Viscosity of Argon: 0.02099 cP (centipoise)
Reynolds Number, R: 7.96 x 10^-5
Friction Factor, f: 8.04 x 10^5
Pressure at outlet: 495 psi
Pressure Drop: 974 psi
Volume Flowrate: 7.85 x 10^-16 l/s
Mass Flowrate: 1.31 x 10-16 kg/s
If we use r=10^-7 m, and v= 10^-4 m/s, we get a centrifugal force F =
m*(V^2)/r of about 0.1 N/kg. The gas flows through an orifice of
about 7.85x10^-15 m^2, at the flow rate of 10^-16 kg/s. With an
effective r of 10^-7 m, the mass of gas accelerating is the volume
(7.85x10^-15 m^2)*(0.5x10-7 m)/2 = 1.963x10^-22 m^3 times the
density, or (1.963x10^-22 m^3) (167 kg/m^3) = 3.28x10^-20 kg. This
gives a very rough thrust per cell of about (0.1 N/kg)(3.28x10^20 kg)
= 3.28x10^-21 N = 3.34x10^-22 kgf. The cell size is about 2x10^-7 m,
or about 5x10^6 per meter, or about 10^20 per m^3. Given 10^20 cells/
m^3, we have (3.34x10^-22 kgf/cell)(10^20 cells/m^3) = 0.0334 kgf or
33.4 grams of thrust per cubic meter of cells. However, if the
inertial mass reduction is only 0.01 percent, then the thrust is only
0.00334 grams of thrust per cubic meter of cells. Not very practical!
I'll update:
http://mtaonline.net/~hheffner/ZPE-CasimirThrust.pdf
with the bad news. Hopefully I got everything right. It's all rough
approximation, but close enough to see the potential value or lack
thereof.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
