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- Head loss = delta P/L = Darcy * p * (Q/A)^2 / (2*D)
- Darcy friction factor for turbulent flow, using Blasius approximation ~= .316 * (Re)^(-1/4)
- Re = Reynold's number = Q*D/(nu*A)
- Q = volumetric flow rate (m^3/s) = .05
- D1 = 2.5" pipe diameter (m) = .0635
- D2 = 3/4" pipe diameter (m) = .01905
- A = pi*D^2/4 = 2.85e-4 m^2
- u air @ 35 degrees C ~= 1.9e-5 kg/(m*s)
- p air = 1.14 kg/m^3
- nu = kinematic viscosity (m^2/s) = u/p = 1.7e-5
- Re = 1.97e5 -> turbulent flow
- Darcy friction factor = .015
- Delta P, D1 = ~4.6 mm H2O/m
- Delta P, D2 = ~1,400 mm H2O/m
- Which seems really high because our pump is only outputting 4000, but the mixing seems satisfactory everywhere along the line.
- I have not accounted for line openings yet.
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