ENGR5002 must memorise

Everything you need in your head for the exam: formulas that are not on the formula sheet, and the definitions examiners ask for. Print it, or cover the right-hand side and test yourself.

Formulas not on the formula sheet

Knudsen number L1 Introduction	$Kn = \frac{\lambda}{L}$	Knudsen number, Mean free path, Characteristic length
Mass density L1 Introduction	$\rho = \frac{m}{V}$	Density, Mass, Volume
Specific weight L1 Introduction	$\gamma = \frac{m g}{V} = \rho g$	Specific weight, Density, Gravitational acceleration
Ideal gas density L1 Introduction	$\rho = \frac{p M}{R T}$	Density, Absolute pressure, Molar mass, Universal gas constant, Absolute temperature

Needed in past-paper solutions

Fanning to Darcy: $f_D = 4 f_{Fanning}$	used in 3 questions, e.g. ENGR217 2017 Q A2, ENGR217 2018 Q B1, ENGR217 2019 Q B3
Moody chart / Colebrook: $\dfrac{1}{\sqrt f} = -2\log_{10}\left(\dfrac{k/D}{3.7} + \dfrac{2.51}{Re\sqrt f}\right)$	used in 3 questions, e.g. ENGR217/266 2021 Q1, ENGR217 2024 Q A1, ENGR217 2025 Q A1
Film theory $k_c = D_{AB}/\delta$ ; penetration theory $k_c = 2\sqrt{D_{AB}/(\pi t_e)}$	used in 2 questions, e.g. ENGR263 2018 Q A3(a), ENGR263 2019 Q A2
Free-surface effect (virtual rise of G): $\Delta GM = \dfrac{\rho_{liq} \sum i}{\rho_{sw} V}$	used in 2 questions, e.g. ENGR217 2017 Q A1, ENGR217 2018 Q B2
Curved surface by equilibrium of a fluid volume: $R = \sqrt{W^2 + F^2}$ , $\tan\theta = W/F$	used in 2 questions, e.g. ENGR217 2017 Q A3, ENGR217 2019 Q B2
Three non-parallel forces in equilibrium are concurrent	used in 2 questions, e.g. ENGR217 2017 Q A3, ENGR217 2019 Q B2
Moody chart / Colebrook: $\dfrac{1}{\sqrt{f_D}} = -2\log_{10}\left(\dfrac{k/D}{3.7} + \dfrac{2.51}{Re\sqrt{f_D}}\right)$	used in 2 questions, e.g. ENGR217 2018 Q B1, ENGR217 2019 Q B3
Composite centroid: $\bar y = \dfrac{\sum A_i y_i}{\sum A_i}$	used in 2 questions, e.g. ENGR217 2019 Q B1, ENGR217 2025 Q A2
Parallel axis theorem: $I = I_G + A d^2$	used in 2 questions, e.g. ENGR217 2019 Q B1, ENGR217 2025 Q A2
Depth of a point on an inclined plane: $z = l \sin\theta$	used in 2 questions, e.g. ENGR217/266 2023 Q A1, Week 1 Exercise 3
Film theory: stagnant film $k_c = \dfrac{D_{AB}}{\delta\,x_{B,lm}}$ ; equimolar or dilute $k_c = \dfrac{D_{AB}}{\delta}$	used in 1 question, e.g. ENGR263 2017 Q A1
Rate = flux x area; mass rate = molar rate x $M$	used in 1 question, e.g. ENGR263 2018 Q A1
Effective diffusivity in a porous solid: $D_{eff} = \dfrac{\varepsilon}{\tau}D_{AB}$ ; Knudsen diffusivity $D_K = \dfrac{d_{pore}}{3}\sqrt{\dfrac{8RT}{\pi M_A}}$	used in 1 question, e.g. ENGR263 2018 Q A3(a)
$N_A = k_c\Delta c_A = k_y\Delta y_A$ ; film theory $k_c = D_{AB}/\delta$ , $k_y = ck_c$ ; $c = P/(RT)$	used in 1 question, e.g. ENGR263 2019 Q A1(b)-(d)
$R = 8314\ \mathrm{J\,kmol^{-1}\,K^{-1}}$	used in 1 question, e.g. ENGR263 2021 Q A2(c)
$1\ \mathrm{atm} = 760\ \mathrm{mm\,Hg}$ ; $1\ \mathrm{dm^3} = 1000\ \mathrm{cm^3}$	used in 1 question, e.g. ENGR263 2022 Q A2(a)-(b)
Le Bas molar volume: $V_A = \sum$ atomic volumes	used in 1 question, e.g. ENGR263 2023 Q A1
Gas solubility in a solid: $c_A = \dfrac{S\,p_A}{22.4\ \mathrm{L/mol}}$ with $S$ in volume (STP) of gas per volume of solid per atm	used in 1 question, e.g. ENGR263 2023 Q A1
$R = 82.06\ \mathrm{cm^3\,atm\,mol^{-1}\,K^{-1}} = 8314\ \mathrm{J\,kmol^{-1}\,K^{-1}}$	used in 1 question, e.g. ENGR263 2023 Q A2(a)-(b)
Non-diffusing B in a liquid film: $N_A = \dfrac{D_{AB}c_{av}}{z}\ln\dfrac{1 - x_{A2}}{1 - x_{A1}} = \dfrac{D_{AB}c_{av}}{z\,x_{BM}}(x_{A1} - x_{A2})$	used in 1 question, e.g. ENGR263 2024 Q A2
Two-film theory, flux continuity at the interface: $N_A = k_y(y - y_i) = k_x(x_i - x)$ , with $y_i = mx_i$ (interface at equilibrium)	used in 1 question, e.g. ENGR262 2018 Q B1(a)-(b)
Overall coefficients: $\dfrac{1}{K_y} = \dfrac{1}{k_y} + \dfrac{m}{k_x}$ , $N_A = K_y(y - y^)$ , $y^ = mx$	used in 1 question, e.g. ENGR262 2018 Q B1(a)-(b)
Individual coefficients $N_A = k_G(p_{A,G} - p_{A,i}) = k_L(c_{A,i} - c_{A,L})$	used in 1 question, e.g. ENGR262 2022 Part B Q A2(b)
Linear equilibrium (Henry) $p_A = Hc_A$ ; $p_A^* = Hc_{A,L}$	used in 1 question, e.g. ENGR262 2022 Part B Q A2(b)
Result: $\dfrac{1}{K_G} = \dfrac{1}{k_G} + \dfrac{H}{k_L}$	used in 1 question, e.g. ENGR262 2022 Part B Q A2(b)
Two-film theory: $N_A = k_y(y - y_i) = k_x(x_i - x)$ , with $(x_i, y_i)$ on the equilibrium curve	used in 1 question, e.g. ENGR262 2025 Q3(b)
Graphical construction: line of slope $-k_x/k_y$ from the bulk point $(x, y)$ to the equilibrium curve	used in 1 question, e.g. ENGR262 2025 Q3(b)
Stability criterion: stable if $GM > 0$ (M above G)	used in 1 question, e.g. ENGR217 2017 Q A1
Metacentric radius: $BM = \dfrac{I}{V}$ ; $GM = BM - BG$	used in 1 question, e.g. ENGR217 2018 Q B2
Heel (inclining) test: $GM = \dfrac{w x}{W \tan\theta}$	used in 1 question, e.g. ENGR217 2018 Q B2
Drag force: $F_D = C_D \tfrac{1}{2}\rho v^2 A$ , A = frontal area for road vehicles	used in 1 question, e.g. ENGR217 2018 Q B3
Power to overcome drag: $P = F_D v$	used in 1 question, e.g. ENGR217 2018 Q B3
Fanning to Darcy: $f_{Darcy} = 4 f_{Fanning}$ , old sheet $H_L = \dfrac{4 f_F L u^2}{2 g D}$	used in 1 question, e.g. ENGR217/266 2021 Q1
Heel (inclining) test: $GM = \dfrac{w\,x}{W \tan\theta}$	used in 1 question, e.g. ENGR217/266 2021 Q2
Metacentric radius: $BM = \dfrac{I}{V}$ , $I$ = second moment of the waterplane area about the roll axis	used in 1 question, e.g. ENGR217/266 2021 Q2
Metacentric height: $GM = OB + BM - OG$ ; stable if $GM > 0$	used in 1 question, e.g. ENGR217/266 2021 Q2
Free-surface effect: reduction in $GM = \dfrac{\rho_{liquid} \sum i}{\rho_{sea} V}$ , $i = \dfrac{l b^3}{12}$ per tank	used in 1 question, e.g. ENGR217/266 2021 Q2
Moment equilibrium about the hinge: $\sum M_O = 0$	used in 1 question, e.g. ENGR217/266 2022 Q A1
Moment equilibrium about the hinge: $\sum M_A = 0$	used in 1 question, e.g. ENGR217/266 2023 Q A1
Pump head: $H = \left(\dfrac{p}{\rho g} + \dfrac{v^2}{2g} + z\right)_{out} - \left(\dfrac{p}{\rho g} + \dfrac{v^2}{2g} + z\right)_{in}$	used in 1 question, e.g. ENGR217 2024 Q A1
Pump similarity (affinity) laws: $\dfrac{Q_2}{Q_1} = \dfrac{N_2}{N_1}\left(\dfrac{D_2}{D_1}\right)^3$ , $\dfrac{H_2}{H_1} = \left(\dfrac{N_2}{N_1}\right)^2\left(\dfrac{D_2}{D_1}\right)^2$	used in 1 question, e.g. ENGR217 2024 Q A2
Lift and drag: $F_L = C_L\,\tfrac{1}{2}\rho u^2 A$ , $F_D = C_D\,\tfrac{1}{2}\rho u^2 A$	used in 1 question, e.g. ENGR217 2024 Q A2
Power to overcome drag: $P = F_D\,u$	used in 1 question, e.g. ENGR217 2024 Q A2
Equal pressure at equal level in one continuous static fluid	used in 1 question, e.g. Week 1 Exercise 2
Components on an inclined plate: $F_H = F\sin\theta$ , $F_V = F\cos\theta$ (equivalently $F_H = \rho g z_{CG} A_{proj}$ , $F_V$ = weight of fluid above)	used in 1 question, e.g. Week 1 Exercise 4
Moment equilibrium about the hinge: $\sum M_B = 0$	used in 1 question, e.g. Week 1 Exercise 4
Floating equilibrium: $F_B = F_g$ , so $D/a = RD_{body}/RD_{liquid}$ for a uniform prism	used in 1 question, e.g. Week 1 Exercise 5
Same pressure at the same level in one continuous static fluid	used in 1 question, e.g. Week 1 Exercise 7
Pressure in a small trapped gas volume is uniform ( $\rho_{air} g h$ negligible)	used in 1 question, e.g. Week 1 Exercise 7
Differential manometer: $p_A - p_B = (\rho_m - \rho) g\,\Delta h$ for A and B at the same level	used in 1 question, e.g. Week 1 Exercise 8
Resultant of two parallel forces: $F_{net} z_{net} = F_1 z_1 - F_2 z_2$	used in 1 question, e.g. Week 1 Exercise 9
Floating equilibrium $F_B = W$ in each liquid	used in 1 question, e.g. Week 1 Exercise 10
Pressure continuous across a static fluid-fluid interface; layer by layer $p = p_{top} + \rho g h$	used in 1 question, e.g. ENGR271 2026 Q1
Piezometer: open column of height $H$ above the tapping, $p = p_{atm} + \rho g H$	used in 1 question, e.g. ENGR271 2026 Q1
Unit conversions: $1\ \mathrm{cm^2/s} = 10^{-4}\ \mathrm{m^2/s}$ ; $R = 8314\ \mathrm{J\,kmol^{-1}\,K^{-1}}$	used in 1 question, e.g. ENGR271 2026 Q3

Definitions

Definition. A is a substance that deforms continuously under the action of a shear stress, however small that stress is.

L1 Introduction

On the formula sheet (know how to use them)

Relative density: $RD = \frac{\rho_{fluid}}{\rho_{water}}$