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Efficiency Slope Comparison
Determining Torque
Torque, Horsepower, Efficiency
Viscosity
Gas Laws
Velocity of Escaping Compressed Air
Absolute Pressure of Steam
Standard Units of Measurement
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Tesla's formula for determining torque (from patent):
"Owing to a number of causes affecting the performance, it is difficult to frame a precise rule which would be generally applicable, but it may be stated that within certain limits, and other conditions being the same, the torque is directly proportionate to the square of the velocity of the fluid relatively to the runner and to the effective area of the disks and, inversely, to the distance separating them. The machine will, generally, perform its maximum work when the effective speed of the runner is one-half of that of the fluid; but to attain the highest economy, the relative speed or slip, for any given performance should be as small as possible. This condition may be to any desired degree approximated by increasing the active area of and reducing the space between the disks."
First of all Tesla was describing a dynamic relationship between his disk turbine – he was not describing an exact mathematical equation. In order to develop an equation that will work across fluids, you must deal with the mass and viscosity of the fluid.
Several equations to start with are:
a) momentum = mass x velocity
b) kinetic energy = (mass x velocity (squared))/2
c) power = torque * angular velocity
Engineers have also developed a working relationship between torque and fluid viscosity in the following equation:
Torque = (3uVr^2)/2h
where:
V = velocity of the fluid in (meters/sec)2pi
u = the viscosity of the fluid (air = .0000179)
r = radius of the disk (in meters)
h = half of the distance between the disks (in meters)
Therefore: Torque (Nm) = (3(.0000179) x 628 x 1*2)/2 x 0.125 x .001 and Torque = 134.9 Nm for the other side of a 1 meter radius disk
- Ken Rieli
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