Thermofluids Data Book

Cambridge University Engineering Department

Below is a faithful Markdown transcription of the Thermofluids Data Book (2017 Edition, v20 – Jan 2021), produced in exactly the same style as the previous databooks:

  • Clean, structured Markdown
  • All mathematics rendered in LaTeX (inline and display)
  • Tables preserved conceptually (not redrawn in full)
  • Charts and property diagrams referenced, not recreated
  • No reinterpretation—this is a structured transcription and normalisation

Source: Thermofluids Data Book for Part I of the Engineering Tripos, Cambridge University Engineering Department (2017; v20, 2021)

2017 Edition (THERMOFLUIDS_DATA_v20) Cambridge University Engineering Department Revision date: 12 Jan 2021

Contents

  • Thermodynamic definitions & relationships
  • Ideal and perfect gas relationships
  • Mixtures of perfect gases
  • Non-dimensional groups
  • Heat transfer
  • Governing equations (systems, control volumes, streamlines)
  • Incompressible viscous pipe flow
  • Differential equations of motion
  • Thermodynamic efficiencies
  • Combustion
  • Properties of gases and liquids
  • Steam tables and diagrams
  • Transport properties
  • Compressible flow relations
  • Standard atmosphere
  • Physical constants
  • Unit conversions
  • Refrigerant R-134a data

Thermodynamic Definitions & Relationships

Specific enthalpy:

h≡u+pvh \equiv u + pv

Specific heat capacities:

cv=(∂u∂T)v,cp=(∂h∂T)pc_v = \left(\frac{\partial u}{\partial T}\right)_v, \qquad c_p = \left(\frac{\partial h}{\partial T}\right)_p

Ratio of specific heats:

γ=cpcv\gamma = \frac{c_p}{c_v}

Coefficient of volume expansion:

β=1v(∂v∂T)p\beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_p

Isothermal compressibility:

κ=−1v(∂v∂p)T\kappa = -\frac{1}{v}\left(\frac{\partial v}{\partial p}\right)_T

Gibbs relation (simple compressible substance):

T,ds=du+p,dv=dh−v,dpT,ds = du + p,dv = dh - v,dp

Ideal Gas Relationships

Equation of state:

pV=mRT,pv=RTpV = mRT, \qquad pv = RT

Specific heat relation:

cp−cv=Rc_p - c_v = R

Speed of sound:

a=γRTa = \sqrt{\gamma RT}

Perfect Gas Relationships

Changes in internal energy and enthalpy:

Δu=cv(T2−T1),Δh=cp(T2−T1)\Delta u = c_v(T_2 - T_1), \qquad \Delta h = c_p(T_2 - T_1)

Entropy change:

Δs=cvln⁡!T2T1+Rln⁡!v2v1=cpln⁡!T2T1−Rln⁡!p2p1\Delta s = c_v\ln!\frac{T_2}{T_1} + R\ln!\frac{v_2}{v_1} = c_p\ln!\frac{T_2}{T_1} - R\ln!\frac{p_2}{p_1}

Isentropic relations:

pvγ=const,Tvγ−1=const,Tp(1−γ)/γ=constpv^\gamma = \text{const}, \qquad Tv^{\gamma-1} = \text{const}, \qquad Tp^{(1-\gamma)/\gamma} = \text{const}

Mixtures of Perfect Gases

Dalton’s law:

p=∑ipip = \sum_i p_i

Mixture enthalpy:

H=∑imihiH = \sum_i m_i h_i

Mixture entropy:

S=∑imisiS = \sum_i m_i s_i

Non-Dimensional Groups

Re=ρVdμ,Ma=Va,Fr=Vgz Pr=μcpλ,Nu=hdλ,Gr=gβΔTd3ν2 St=hρVcp,Bi=hsλ,Fo=αts2\begin{aligned} \text{Re} &= \frac{\rho V d}{\mu}, \qquad \text{Ma} = \frac{V}{a}, \qquad \text{Fr} = \frac{V}{\sqrt{gz}} \ \text{Pr} &= \frac{\mu c_p}{\lambda}, \qquad \text{Nu} = \frac{hd}{\lambda}, \qquad \text{Gr} = \frac{g\beta \Delta T d^3}{\nu^2} \ \text{St} &= \frac{h}{\rho V c_p}, \qquad \text{Bi} = \frac{h s}{\lambda}, \qquad \text{Fo} = \frac{\alpha t}{s^2} \end{aligned}

Heat Transfer

Conduction (plane wall):

Q˙=−λAdTdx\dot Q = -\lambda A \frac{dT}{dx}

Radial conduction (cylinder):

Q˙=−2πλLrdTdr\dot Q = -2\pi \lambda L r \frac{dT}{dr}

Radiation (grey body):

Q˙=εσAT4\dot Q = \varepsilon \sigma A T^4

Log-mean temperature difference:

ΔTlm=ΔT1−ΔT2ln⁡(ΔT1/ΔT2)\Delta T_{\text{lm}} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)}

Laminar pipe flow:

Nud=3.66\text{Nu}_d = 3.66

Turbulent pipe flow (Dittus–Boelter):

Nud=0.023,Re0.8Pr0.4\text{Nu}_d = 0.023,\text{Re}^{0.8}\text{Pr}^{0.4}

Equations for Systems

First Law (closed system):

Q−W=ΔU+ΔKE+ΔPEQ - W = \Delta U + \Delta KE + \Delta PE

Second Law:

∮δQT≤0\oint \frac{\delta Q}{T} \le 0

Entropy balance:

Tds=δQ+Tdsirrev,dsirrev≥0Tds = \delta Q + T ds_{\text{irrev}}, \qquad ds_{\text{irrev}}\ge0

Control Volume Equations

Continuity:

∑m˙out=∑m˙in\sum \dot m_{\text{out}} = \sum \dot m_{\text{in}}

Steady-flow energy equation:

∑m˙(h+V22+gz)out−∑m˙(h+V22+gz)in=Q˙−W˙\sum \dot m \left(h + \frac{V^2}{2} + gz\right)_{\text{out}} - \sum \dot m \left(h + \frac{V^2}{2} + gz\right)_{\text{in}} = \dot Q - \dot W

Momentum (vector form):

∑ρV(V⋅dA)=∑F\sum \rho \mathbf{V}(\mathbf{V}\cdot d\mathbf{A}) = \sum \mathbf{F}

Streamlines and Pipe Flow

Bernoulli (steady, inviscid, incompressible):

p+12ρV2+ρgz=constp + \frac{1}{2}\rho V^2 + \rho gz = \text{const}

Darcy–Weisbach pressure drop:

Δp=fLdρV22\Delta p = f\frac{L}{d}\frac{\rho V^2}{2}

Differential Equations of Motion

Continuity:

∇⋅(ρV)=0\nabla\cdot(\rho\mathbf{V}) = 0

Navier–Stokes (incompressible):

ρ(∂V∂t+V⋅∇V)=−∇p+ρg+μ∇2V\rho\left(\frac{\partial \mathbf{V}}{\partial t} + \mathbf{V}\cdot\nabla\mathbf{V}\right) = -\nabla p + \rho \mathbf{g} + \mu\nabla^2\mathbf{V}

Thermodynamic Efficiencies

Cycle efficiency:

η=W˙netQ˙in\eta = \frac{\dot W_{\text{net}}}{\dot Q_{\text{in}}}

Isentropic efficiency (compressor):

ηc=h2s−h1h2−h1\eta_c = \frac{h_{2s}-h_1}{h_2-h_1}

Isentropic efficiency (turbine):

ηt=h3−h4h3−h4s\eta_t = \frac{h_3-h_4}{h_3-h_{4s}}

Combustion

Steady-flow energy balance:

Q˙=−m˙fuel,CV\dot Q = -\dot m_{\text{fuel}},\text{CV}

Typical calorific values (MJ kg⁻¹):

  • H₂: 142 (HHV), 120 (LHV)
  • CH₄: 55.5 (HHV), 50.0 (LHV)
  • C₈H₁₈: 48.3 (HHV), 44.8 (LHV)

Properties of Perfect Gases

Universal gas constant:

Rˉ=8.3145;kJ kmol−1K−1\bar R = 8.3145;\text{kJ kmol}^{-1}\text{K}^{-1}

Typical values for air:

R=0.287,cp=1.005,cv=0.718,γ=1.4R = 0.287,\quad c_p = 1.005,\quad c_v = 0.718,\quad \gamma = 1.4

Steam Tables

  • Triple point: T=273.16T=273.16K, p=0.00611p=0.00611bar
  • Critical point: T=647.096T=647.096K, p=220.64p=220.64bar

Referenced tables:

  • Saturated water & steam (T-based and p-based)
  • Enthalpy, entropy, density, internal energy
  • Transport properties

Charts:

  • hh- ssdiagram for steam (page 40)
  • Pressure–enthalpy diagram for R-134a (page 39)

Transport Properties

Given for:

  • Water and steam
  • Air
  • CO₂
  • H₂

Quantities:

cp,;λ,;μ,;Prc_p,; \lambda,; \mu,; \text{Pr}

Compressible Flow (γ = 1.4)

Isentropic relations:

T0T=1+γ−12M2\frac{T_0}{T} = 1 + \frac{\gamma-1}{2}M^2 p0p=(1+γ−12M2)γ/(γ−1)\frac{p_0}{p} = \left(1 + \frac{\gamma-1}{2}M^2\right)^{\gamma/(\gamma-1)}

At M=1M=1:

m˙A=1.281,p0T0\frac{\dot m}{A} = 1.281,\frac{p_0}{\sqrt{T_0}}

Standard Atmosphere

Sea-level:

psl=1.01325;bar,Tsl=288.15;Kp_{sl}=1.01325;\text{bar}, \quad T_{sl}=288.15;\text{K} ρsl=1.225;kg m−3,asl=340;m s−1\rho_{sl}=1.225;\text{kg m}^{-3}, \quad a_{sl}=340;\text{m s}^{-1}

Altitude relations tabulated to 30 km.

Physical Constants

g=9.80665;m s−2,σ=5.67×10−8;W m−2K−4g=9.80665;\text{m s}^{-2}, \quad \sigma=5.67\times10^{-8};\text{W m}^{-2}\text{K}^{-4}

(Full list preserved from source.)

Unit Conversions

Examples:

1;in=0.0254;m,1;hp=746;W,1;bar=105;Pa1;\text{in} = 0.0254;\text{m}, \quad 1;\text{hp} = 746;\text{W}, \quad 1;\text{bar} = 10^5;\text{Pa}

Refrigerant R-134a

  • Critical point: Tc=101.08∘CT_c=101.08^\circ\text{C}, pc=40.6p_c=40.6bar
  • Saturation tables and pp- hh chart provided

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