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Figure 5-9 design condition Tsd 120 67.5 T red numbers used in example 4.22MMBtu⎛ 293KWHR⎞ ⎛ $0.11 ⎞ = $136 / s ⎜⎝ M M B t u ⎟⎠ ⎜⎝ K W H R ⎟⎠ ∆Td TL = d (T−T )−Q Q inbldg ∆ Td i out i od 67.5 ⎛293KWHR⎞⎛ $0.11 ⎞9 4.22(TMoMutB)otuutdoor temperature (=oF$)136 / seas ⎜⎝ M M B t u ⎟⎠ ⎜⎝ K W H R ⎟⎠ ⎛Tsd −Tin ⎞ Figure 5-8 design condition Qd 75,000 red numbers used in example ∆Td Tin (Tout)outdoor temperature (oF) ⎛ 293KWHR ⎞ ⎛ $0.11 ⎞ 67.5 9 Instantaneous building space heating load: Lbldg=Qd (Ti−Tout)−Qi ∆Td Where: L = instantaneous building space heating load (Btu/hr) bldg ⎛ 293KWHR ⎞ ⎛ $0.11 ⎞ Q = building4’s.2d2eMsigMnBstpuace heating load (Btu/hr) = $136 / d⎜⎟⎜⎟ ⎛ T − ⎝ T M⎞ M B t u ⎠ ⎝ K W H R ⎠ ∆T = difference between inside and outside temperature d Ts =⎜ sd in ⎟(Tin −Tout)+Tin at design load (oF) ⎝ Tin − Tod ⎠ Tin = indoor setpoint temperature for space heating (oF), typically assumed at 70oF Q() Q = current rate of inte∆rTnal heat gain (Btu/hr) ( T = current outdoor temperature (oF) out Lbldg= d Ti−Tout −Qi )2 Supply water temperature to space heating distribution: i Qh=⎡⎣k1+dk2(Ts)⎤⎦+k3(Tout)+k4 Tout ⎛T−T⎞ ( )2 TCO=P=⎡c+c(T)−⎤T+c)(T+T)+c T s ⎜ sd⎣ 1 in ⎟2 isn ⎦ out3 ambin 4 amb ⎝Tin −Tod ⎠ Where: Ts = currently required supply water temperature (oF) T = required supply water temperate at design loa9d5%(oFo) f lo in Qh =⎡⎣k1+k2(Ts)⎤⎦+k3(Tout)+k4 Tout Tsd = indoor setpoint temperature for space he(ating)2 (oF), typically assumed at 70oF ⎡ 0.95 × 194.3 × 43.6 seasonal heating cost = T = outdoor temperature at design load (oF) Tod outb = current outdoor temperature (oF)⎢⎣ 3.49 Q Heating capacityd of heat pump: Lbldg = ∆T (Ti −Tout )−Qi Q=⎡k+k(T)⎤+k(T )+k T d ( )2 h⎣12s⎦3out 4out ⎛T−T⎞ Where: Q =“insTta=ntaneous”hea(tTing−cTapa)c+ityTofheatpump(Btu/hr) s ⎜sd in⎟in out in season ⎝T −T ⎠ 2 h T = currentlyin reqoudired supply water temperature to s COP=⎡c+c(T)⎤+c(T )+c(T ) ⎣12s⎦3amb 4amb distribution system (oF) Tout = current outdoor temperature (oF) k1, k2, k3, k4 = constants determined by curve fitting to 2 manufacQtur=er⎡’skp+ubklis(hTed)⎤h+eakt (cTapa)c+itykc(uTrves). h ⎣ 1 2 s ⎦ 3 out 4 out 95% of lo COP of heat pump: ⎡ 0.95 × 194.3 × 43.66 seasonal heating cost = ⎢ Where: heat pump COP = “instantaneous” COP of heat pump (Btu/hr) Ts = currently required supply water temperature to distribution system (oF) ad by heat pump Tamb=currentoutdoortemperat⎡u0re.9(o5F×)194.3×43.66⎤ seasonal heating cost = + c1, c2, c3, c4 = constants deter⎢mined by curve fitting⎥to 6 ⎤ma⎡n0u.0fa5c×tu1re9r4’s.3p×ub4l3is.h6e6d⎤ heat capacity curves. seasonal heating cost = × ⎥+⎢ 1 ⎥=$2,733⎜⎝MMBtu⎟⎠ ⎜⎝ sea ⎦⎣⎦ seasonal average COP provided by 95% of load b ⎣ 3.49 ⎦ ⎛$16.85⎞ ⎛194.3 COP=⎡c+c(T)⎤+c(T⎣)+c(T )2 ⎦ ⎣12s⎦3amb 4amb 3.49 seasonal average COP 4.22 MMBtu ⎜⎝ MMBtu ⎟⎠ ⎜⎝ KWHR ⎟⎠ = $136 / season Ts =⎜⎝Tin −Tod ⎟⎠(Tin −Tout)+Tin COP = ⎡⎣c1 + c2 (Ts )⎤⎦ + c3(Tamb ) + c4 Tamb seasonal average COP ( )2 provided by heat pump provi aux heat provided by heat pump aux elec. provided by p h eason on ad by heat ⎤+⎡0.05× ⎥ ⎢⎣ y heat pum ⎡0.05×19 ⎢⎣ MMBtu⎞ = son ⎟⎠ 95% of load by heat pump heat source 43 q=k(T −T ) wa room seasonal heating cost = ⎛⎜ $16.85 ⎞⎟ × ⎛⎜ 194.3 MMBtu ⎞⎟ = $3, (Lbldg) building heating load (Btu/hr) (Ts) supply water temperature (oF)PDF Image | Heat Pump Systems 2020
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