Thermodynamics
• pV = nRT ||pV = mrT ||pv = rT
• pv κ = C te (isentropic)
k−1 k
• T2,s = pp21 T1 (isentropic)
• ∆h = cp ∆T
• r = cp − cv (ideal gas)
• ηcarnot = 1 − Tcold
Thot
• dW = pdV (work)
• W1,2s = U2,s − U1 = m2,s cv (T2,s − T1 ) (internal energy)
Wisentropic
• ηs = Wreal ||ηturb,s = h3 −h4
h3 −h4s (isentropic efficiency)
Fluid Mechanics
• A1 v 1 = A2 v 2
• p + 12 ρv 2 + ρgh = cte
p1 −p2 v12 −v22
• ρ + 2 + g(z1 − z2 ) = hl,major + hl,minor − ∆hpump (energy equation) (* m = power)
2 2 ∆ppump hl,T ot
L v v
with: hl,major = f D 2 ||hl,minor = K 2 ||∆hpump = ρ ||Hl,T ot = g
∆ppump
• Ppump = ṁ = Q̇∆ppump ||Ppump = ṁg(Ha + Hf + Hp + ∆z)
ρ
• Pturb = ṁ(h1 − h2 ) = ṁcp (T1 − T2 )
2
• ∆ppipe = f D
L ρv
2
• ∆p = ∆ρgh
• Q̇ = vA||ṁ = ρvA
• Fair = 12 ρv 2 CD A
−g∆h
• Thigh − Tlow = cP (temp. diff. by height)
• D= 4A
P (hydraulic diameter)
Heat Transfer
• Q̇ = ∆T
Rth,tot
ln(rout /rin )
• Rcond,wall = x
kA ||Rcond,cylinder = 2πkL ||Rcond,sphere = rout −rin
4πkrout rin
• Q̇conv = hA(Ts − T∞ )
• Rconv = 1
hA
• Q̇radiation = ϵσA(Thot
4 4
− Tcold )
• Q̇ = ṁ∆h = ṁcp ∆T
• Q̇vapor = ṁ∆hlatent
• Q̇loss = P (1 − η)
• COP = Q
W = Q̇
P ||COPheatpump ≈ 3||COPcarnot,cooling = Tcold
Thot −Tcold ||COPcarnot,heating = Thot
Thot −Tcold
• Cth,storage = mcp = ρVstorage cp
• Rth = 1
UA
• Q̇heat−exchanger = U A∆Tlm = U A ∆T1 −∆T
∆T1
2
ln( ∆T )
2
1
• pV = nRT ||pV = mrT ||pv = rT
• pv κ = C te (isentropic)
k−1 k
• T2,s = pp21 T1 (isentropic)
• ∆h = cp ∆T
• r = cp − cv (ideal gas)
• ηcarnot = 1 − Tcold
Thot
• dW = pdV (work)
• W1,2s = U2,s − U1 = m2,s cv (T2,s − T1 ) (internal energy)
Wisentropic
• ηs = Wreal ||ηturb,s = h3 −h4
h3 −h4s (isentropic efficiency)
Fluid Mechanics
• A1 v 1 = A2 v 2
• p + 12 ρv 2 + ρgh = cte
p1 −p2 v12 −v22
• ρ + 2 + g(z1 − z2 ) = hl,major + hl,minor − ∆hpump (energy equation) (* m = power)
2 2 ∆ppump hl,T ot
L v v
with: hl,major = f D 2 ||hl,minor = K 2 ||∆hpump = ρ ||Hl,T ot = g
∆ppump
• Ppump = ṁ = Q̇∆ppump ||Ppump = ṁg(Ha + Hf + Hp + ∆z)
ρ
• Pturb = ṁ(h1 − h2 ) = ṁcp (T1 − T2 )
2
• ∆ppipe = f D
L ρv
2
• ∆p = ∆ρgh
• Q̇ = vA||ṁ = ρvA
• Fair = 12 ρv 2 CD A
−g∆h
• Thigh − Tlow = cP (temp. diff. by height)
• D= 4A
P (hydraulic diameter)
Heat Transfer
• Q̇ = ∆T
Rth,tot
ln(rout /rin )
• Rcond,wall = x
kA ||Rcond,cylinder = 2πkL ||Rcond,sphere = rout −rin
4πkrout rin
• Q̇conv = hA(Ts − T∞ )
• Rconv = 1
hA
• Q̇radiation = ϵσA(Thot
4 4
− Tcold )
• Q̇ = ṁ∆h = ṁcp ∆T
• Q̇vapor = ṁ∆hlatent
• Q̇loss = P (1 − η)
• COP = Q
W = Q̇
P ||COPheatpump ≈ 3||COPcarnot,cooling = Tcold
Thot −Tcold ||COPcarnot,heating = Thot
Thot −Tcold
• Cth,storage = mcp = ρVstorage cp
• Rth = 1
UA
• Q̇heat−exchanger = U A∆Tlm = U A ∆T1 −∆T
∆T1
2
ln( ∆T )
2
1
