Raphi Giangiulio's Homemade Pipe Organ

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Calculating the Flowrate Requirement for a Pipe

The velocity of the air leaving the mouth is a function of the pressure only. This may seem counterintuitive at first because everyone knows that when you knozzle the end of a hose by reducing the area of the exit hole, you increase the velocity of the water. This is true but what you're actually doing is increasing the pressure when you knozzle something. The velocity is calculated by the following equation:

V = [2 * P / ρ]^0.5

  • V is the velocity of the air leaving the mouth
  • ρ is the density of air
  • P is the pressure

The flowrate Q is equal to the area times the velocity:

Q = A * V

Where the area is the internal width of the pipe times the windsheet thickness:

A = IW * WST

Put it all together and you get:

Q = IW * WST * [2 * P / ρ]^0.5

Assuming the density of air is 1.2 kg/m3 and adding a factor for units gives you:

Q = 27.86 * IW * WST * [P^0.5]

  • Q is the flowrate in cubic feet per minute (CFM)
  • IW is the internal width of the pipe in inches
  • WST is the windsheet thickness in inches
  • P is the air pressure in inches of water

The equation assumes that the pipe is unrestricted at the foot.

Here's an example. My CCC Soubasse pipe has an internal width of 4.724, the windsheet thickness is 0.060 and the pressure is 2 inches of water.

Q = 27.86 * 4.724 * 0.060 * [2^0.5]

Q = 11.2 CFM