Phoenix Turbine Builders Club

Useful Charts & Data

Determining Torque

Torque, Horsepower, Efficiency

Viscosity

Gas Laws

Velocity of Escaping Compressed Air

Absolute Pressure of Steam

Standard Units of Measurement

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

Viscosity

Viscosity is the force exerted by layers of fluid passing over each other. Measurement is in poise (†) or centipoise, named after the Frenchman Poiseuille. 

One poise equals 1 dyne-sec/cm².

The Poiseuille equation relates flow volume to viscosity, pressure drops and physical characteristics of the pipe.

Q = (P₂ - P₁)BR⁴
       8L†

P = pressure

R = pipe radius

L = pipe length

Gas Laws

The combining of Boyle's Law with Charles' Law results in the General Gas Law:

P₁V₁  =  P₂V₂
  T₁            T₂    

Charles' Law is:

V_{1  =}  V₂
T_{1  =}  T₂

V = volume

T = absolute temperature °C + 273

The volume of gas is proportional to the temperature. The higher the temperature, the greater the volume if pressure is constant.

The volume of a fixed mass of gas at constant temperature is inversely proportional to the pressure. If pressure goes up, volume goes down. The value of pressure times volume becomes constant.

P₁V₁  =  P₂V₂

Standard Units of Measurement