Mathematical model Rotating furnace

rotation speed , focal length

the focal length of paraboloid related angular speed @ liquid rotated equation:



2
f

ω

2


=
g


{\displaystyle 2f\omega ^{2}=g}

,



f


{\displaystyle f}

focal length,



ω


{\displaystyle \omega }

rotation speed, ,



g


{\displaystyle g}

acceleration due gravity. must in compatible units so, example,



f


{\displaystyle f}

can in metres,



ω


{\displaystyle \omega }

in radians per second, ,



g


{\displaystyle g}

in metres per second-squared. angle unit in



ω


{\displaystyle \omega }

must radians. 1 radian per second 9.55 rotations per minute (rpm). on earth s surface,



g


{\displaystyle g}

9.81 metres per second-squared. putting these numbers equation produces approximation:



f

s

2


≈
447


{\displaystyle fs^{2}\approx 447}

,



f


{\displaystyle f}

focal length in metres, ,



s


{\displaystyle s}

rotation speed in rpm.