Derivation of HVAC equation
Derivation of HVAC equation
(OP)
First of all, what is the name of this equation:
ΔT = SPtotal / (2.7*ηf)
This is used in HVAC applications to determine the total temperature rise across the supply fan.
Where:
ΔT = change in temperature (F)
SP = Total Static Pressure (inH2O)
ηf = fan efficiency (decimal form)
And where is this derived from? Can someone provide a link or specifics?
I started off with the first law:
Assume:
m_dot(1) = m_dot(2) = m_dot
Δz = 0
ΔU = 0 = Q - W + m_dot(Δh + 0.5(ΔV2))
Δh = cpΔT
m_dot = ρAV
This seemed to get me nowhere...so I went to Bernoulli's (neglect altitude change)
(P1/ρ) + 0.5(V12) = (P2/ρ) + 0.5(V22)
ΔP = 0.5ρ(ΔV2)
but I see nowhere where temperature is involved...im lost.
ΔT = SPtotal / (2.7*ηf)
This is used in HVAC applications to determine the total temperature rise across the supply fan.
Where:
ΔT = change in temperature (F)
SP = Total Static Pressure (inH2O)
ηf = fan efficiency (decimal form)
And where is this derived from? Can someone provide a link or specifics?
I started off with the first law:
Assume:
m_dot(1) = m_dot(2) = m_dot
Δz = 0
ΔU = 0 = Q - W + m_dot(Δh + 0.5(ΔV2))
Δh = cpΔT
m_dot = ρAV
This seemed to get me nowhere...so I went to Bernoulli's (neglect altitude change)
(P1/ρ) + 0.5(V12) = (P2/ρ) + 0.5(V22)
ΔP = 0.5ρ(ΔV2)
but I see nowhere where temperature is involved...im lost.





RE: Derivation of HVAC equation
RE: Derivation of HVAC equation
Page 5, equation 12
http://www.learningincontext.com/PiC-Web/pdfs/AirS...
RE: Derivation of HVAC equation
RE: Derivation of HVAC equation
Did you look into applying the ideal gas law at the end of your original post derivation? That should get you to temperature...
Best to you,
Goober Dave
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RE: Derivation of HVAC equation
RE: Derivation of HVAC equation
I actually just experienced this at work. You had it right by following the 1st Law, but you must also neglect Kinetic Energy as the Velocities are essentially the same. With that you will be left with Work equal to mass flow times change in enthalpy. Then remember that mass floe rate is (density*Area*Velocity) and that enthalpy is (cp*change in temperature).
Density is 0.075, cp is 0.24 and the rest is converting to inH2O
RE: Derivation of HVAC equation
You cannot get Deg. F by dividing static pressure by a pure number (fan efficiency). Temperature rise (english units) = BTUH/(cfm*1.08).
Remember Heat rate = mass flow x Heat Capacity x Change in temperature.
Then, change in temp = Heat rate/(mass flow x heat capacity).
RE: Derivation of HVAC equation
Don't forget that it's heat of compression plus paddlewheel work being done (fan inefficiency). Throw it together, consolidate the constants, and you're almost there.
Best to you,
Goober Dave
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