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
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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 \equiv u + pv ]

Specific heat capacities: [ c_v = \left(\frac{\partial u}{\partial T}\right)_v, \qquad c_p = \left(\frac{\partial h}{\partial T}\right)_p ]

Ratio of specific heats: [ \gamma = \frac{c_p}{c_v} ]

Coefficient of volume expansion: [ \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_p ]

Isothermal compressibility: [ \kappa = -\frac{1}{v}\left(\frac{\partial v}{\partial p}\right)_T ]

Gibbs relation (simple compressible substance): [ T,ds = du + p,dv = dh - v,dp ]

Ideal Gas Relationships

Equation of state: [ pV = mRT, \qquad pv = RT ]

Specific heat relation: [ c_p - c_v = R ]

Speed of sound: [ a = \sqrt{\gamma RT} ]

Perfect Gas Relationships

Changes in internal energy and enthalpy: [ \Delta u = c_v(T_2 - T_1), \qquad \Delta h = c_p(T_2 - T_1) ]

Entropy change: [ \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: [ pv^\gamma = \text{const}, \qquad Tv^{\gamma-1} = \text{const}, \qquad Tp^{(1-\gamma)/\gamma} = \text{const} ]

Mixtures of Perfect Gases

Dalton’s law: [ p = \sum_i p_i ]

Mixture enthalpy: [ H = \sum_i m_i h_i ]

Mixture entropy: [ S = \sum_i m_i s_i ]

Non-Dimensional Groups

[ \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): [ \dot Q = -\lambda A \frac{dT}{dx} ]

Radial conduction (cylinder): [ \dot Q = -2\pi \lambda L r \frac{dT}{dr} ]

Radiation (grey body): [ \dot Q = \varepsilon \sigma A T^4 ]

Log-mean temperature difference: [ \Delta T_{\text{lm}} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)} ]

Laminar pipe flow: [ \text{Nu}_d = 3.66 ]

Turbulent pipe flow (Dittus–Boelter): [ \text{Nu}_d = 0.023,\text{Re}^{0.8}\text{Pr}^{0.4} ]

Equations for Systems

First Law (closed system): [ Q - W = \Delta U + \Delta KE + \Delta PE ]

Second Law: [ \oint \frac{\delta Q}{T} \le 0 ]

Entropy balance: [ Tds = \delta Q + T ds_{\text{irrev}}, \qquad ds_{\text{irrev}}\ge0 ]

Control Volume Equations

Continuity: [ \sum \dot m_{\text{out}} = \sum \dot m_{\text{in}} ]

Steady-flow energy equation: [ \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): [ \sum \rho \mathbf{V}(\mathbf{V}\cdot d\mathbf{A}) = \sum \mathbf{F} ]

Streamlines and Pipe Flow

Bernoulli (steady, inviscid, incompressible): [ p + \frac{1}{2}\rho V^2 + \rho gz = \text{const} ]

Darcy–Weisbach pressure drop: [ \Delta p = f\frac{L}{d}\frac{\rho V^2}{2} ]

Differential Equations of Motion

Continuity: [ \nabla\cdot(\rho\mathbf{V}) = 0 ]

Navier–Stokes (incompressible): [ \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: [ \eta = \frac{\dot W_{\text{net}}}{\dot Q_{\text{in}}} ]

Isentropic efficiency (compressor): [ \eta_c = \frac{h_{2s}-h_1}{h_2-h_1} ]

Isentropic efficiency (turbine): [ \eta_t = \frac{h_3-h_4}{h_3-h_{4s}} ]

Combustion

Steady-flow energy balance: [ \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: [ \bar R = 8.3145;\text{kJ kmol}^{-1}\text{K}^{-1} ]

Typical values for air: [ R = 0.287,\quad c_p = 1.005,\quad c_v = 0.718,\quad \gamma = 1.4 ]

Steam Tables

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

Referenced tables:

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

Charts:

  • (h!-!s) diagram for steam (page 40)
  • Pressure–enthalpy diagram for R-134a (page 39)

Transport Properties

Given for:

  • Water and steam
  • Air
  • CO₂
  • H₂

Quantities: [ c_p,; \lambda,; \mu,; \text{Pr} ]

Compressible Flow (γ = 1.4)

Isentropic relations: [ \frac{T_0}{T} = 1 + \frac{\gamma-1}{2}M^2 ]

[ \frac{p_0}{p} = \left(1 + \frac{\gamma-1}{2}M^2\right)^{\gamma/(\gamma-1)} ]

At (M=1): [ \frac{\dot m}{A} = 1.281,\frac{p_0}{\sqrt{T_0}} ]

Standard Atmosphere

Sea-level: [ p_{sl}=1.01325;\text{bar}, \quad T_{sl}=288.15;\text{K} ]

[ \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;\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;\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: (T_c=101.08^\circ\text{C}), (p_c=40.6) bar
  • Saturation tables and (p!-!h) chart provided

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