Equations, Properties and Constants Flashcards
BHP = GPM x TDH(ft) x SG / (3960 x η-pump)
Derive 3960
3960 = 33,000 / 8.34
* 33,000 ftlbs/min/hp
* 8.34 lb/gal = density of water at 54 degF
See NCEES handbook table 1.2.9 for water properties at atmospheric pressure
BTUh = GPM x 500 x dT.
Derive the 500 constant
500 = 8.34 lb/gal x 60min/hr x 1 Btu/lb/deg F
* 8.34 lb/gal = density of water at 54 degF
* Cp = 1 Btu/lb/deg F = Specific heat of water
See NCEES handbook table 1.2.9 for water properties at atmospheric pressure
What is the standard air density at sea level and 68°F (20°C)?
0.075 lb/ft³ (1.2 kg/m³)
See NCEES handbook table 1.2.1 for air properties at atmospheric pressure
What is the formula for calculating the sensible heat load?
Qs = 1.08×CFM×ΔT
(where 𝑄𝑠 is sensible heat in BTU/hr, CFM is airflow, and Δ𝑇 is temperature difference in °F).
See NCEES handbook table 1.2.1 for air properties at atmospheric pressure
Derive the 1.085 constant in the sensible heat equation (Qs=1.085xCFMxΔT)
1.085 = 0.243 Btu/lb/degF x 60min/hr / 13.5 ft3/lb
* Cp = 0.24 Btu/lb/degF = specific heat of moist air at std conditions
* 13.5 ft3/lb = specific volume of air at std conditions
Divide 60 by 13.5 ft3/lb or multiply by 0.075 lb/ft3 (density of air)
See NCEES handbook table 1.2.1 for air properties at atmospheric pressure
What is the formula for calculating the latent heat load?
Ql (Btuh) = 0.69xCFMxΔw (gr/lb)
* Δw = humidity ratio difference
See NCEES handbook table 1.2.1 for air properties at atmospheric pressure
Ql (Btuh) = 0.69xCFMxΔw (gr/lb)
Derive the 0.69 constant.
0.69 = (60min/hr / 13.5 ft3/lb) x (1076 Btu/lb / 7000 gr/lb)
* 13.5 ft3/lb = specific volume of air at std conditions
* 1076 Btu/lb = Δhevap (latent heat of vaporization at std conditions)
* 7000 gr/lb = grains per lb of dry air
Divide 60 by 13.5 ft3/lb or multiply by 0.075 lb/ft3 (density of air)
What is the total heat gain equation?
Qt(Btuh) = 4.5xCFMxΔh
* Δh = enthalpy difference (Btu/lb)
Derive 4.5 in the total heat gain equation
4.5 = 0.075 lb/ft3 x 60 min/hr
Divide 60 by 13.5 ft3/lb or multiply by 0.075 lb/ft3 (density of air)
See NCEES handbook table 1.2.1 for air properties at atmospheric pressure
What is the equation for fan brake horsepower?
BHP (fan) = CFM x SP (“wg) x SG / (6356 x η-fan)
Derive 6356 in the fan brake horsepower equation
6356 = 33,000 / (62.3/12)
* 33,000 ftlbs/min/hp
* 62.3 = lbs/ft3 water density
* 12 in/ft
Calculate electrical (motor) HP from BHP
Motor HP = BHP / η-Motor
Motor HP should be greater than BHP
Calculate electrical (motor) HP from hydraulic HP
Motor HP = Hydraulic HP / (η-motor x η-pump)
BHP = Hydraulic HP / η-pump
What is the COP
COP = Coefficient of Performance
COP = Evaporator Energy (kW) / Compressor Work (kW)
COP is the ratio of how much cooling is provided over the input power
What is the EER
EER = Energy Efficiency Ratio
EER = Cooling energy (Btu) / compressor work (kW)
EER = COP x 3.412
What is the equation for compressor efficiency
η-comp = h(ideal, lvg) - h(ent) / h(act) - h(ent)
* h = enthalpy
* h(ideal, lvg) = enthalpy leaving compressor after following constant entropy from entering compressor pressure
What is the specific heat of air at constant pressure and standard conditions?
cp = 0.24 btu/lb-degF
What is the density of water at standard conditions?
62.4 lbm/ft^3
What is the specific heat Cp of water at standard conditions?
1 BTU/lb-degF (at 68 degF)
What does specific heat represent?
The amount of heat required to raise the temperature of a material by 1 degree. Also referred to as heat capacity.
What does specific gravity (SG) represent?
Ratio of the density of a material to the density of water (62.4 lbm/ft^3). Dimensionless.
SG of water = 1
Calculate the COP for a refrigerant cycle
COP = h1-h4 / h2-h1
* h1 = enthalpy leaving evaporator
* h2 = enthalpy leaving compressor
* h4 = enthalpy entering evaporator (h3=h4 due to const. enthalpy process)
What is the specific volume of dry air at sea level?
13.35 ft^3/lb dry air
What is the affinity law for flow rate, given motor RPM?
RPM1/RPM2 = GPM1/GPM2
