Glossary of engineering: A–L

${\displaystyle y'+P(x)y=Q(x)y^{n}\,}$

${\displaystyle n}$

${\displaystyle n\neq 0}$

${\displaystyle n\neq 1}$

${\displaystyle k={\frac {R}{N_{\text{A}}}}.}$.

${\displaystyle \mathbf {R} =n_{1}\mathbf {a} _{1}+n_{2}\mathbf {a} _{2}+n_{3}\mathbf {a} _{3}}$

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} T}}={\frac {L}{T\,\Delta v}}={\frac {\Delta s}{\Delta v}},}$

${\displaystyle \mathrm {d} P/\mathrm {d} T}$

${\displaystyle L}$

${\displaystyle T}$

${\displaystyle \Delta v}$

${\displaystyle \Delta s}$

${\displaystyle \oint {\frac {\delta Q}{T_{surr}}}\leq 0,}$

where ${\displaystyle \delta Q}$ is the infinitesimal amount of heat absorbed by the system from the reservoir and ${\displaystyle T_{surr}}$ is the temperature of the external reservoir (surroundings) at a particular instant in time. In the special case of a reversible process, the equality holds.[114] The reversible case is used to introduce the entropy state function. This is because in a cyclic process the variation of a state function is zero. In words, the Clausius statement states that it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir.[115] Equivalently, heat spontaneously flows from a hot body to a cooler one, not the other way around.[116] The generalized "inequality of Clausius"[117]

${\displaystyle dS>{\frac {\delta Q}{T_{surr}}}}$

${\displaystyle 1~{\text{C}}=1~{\text{A}}\cdot 1~{\text{s}}}$

Thus, it is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt:

${\displaystyle 1~{\text{C}}=1~{\text{F}}\cdot 1~{\text{V}}}$

The coulomb is equivalent to the charge of approximately 6.242×10¹⁸ (1.036×10⁻⁵ mol) protons, and −1 C is equivalent to the charge of approximately 6.242×10¹⁸ electrons.

${\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}}$,

where k_e is the Coulomb constant (k_e ≈ 9×10⁹ N⋅m²⋅C⁻²), q₁ and q₂ are the signed magnitudes of the charges, and the scalar r is the distance between the charges. The force of the interaction between the charges is attractive if the charges have opposite signs (i.e., F is negative) and repulsive if like-signed (i.e., F is positive).

• an applied force (the deformation energy in this case is transferred through work) or
• a change in temperature (the deformation energy in this case is transferred through heat).

The first case can be a result of tensile (pulling) forces, compressive (pushing) forces, shear, bending or torsion (twisting).

${\displaystyle \rho ={\frac {m}{V}}}$

${\displaystyle w(x)}$

${\displaystyle V(x)=-\int w(x)\,dx}$

The internal moment M(x) is the integral of the internal shear:

${\displaystyle M(x)=\int V(x)\,dx}$ = ${\displaystyle -\int [\int w(x)\ \,dx]dx}$

The angle of rotation from the horizontal, ${\displaystyle \theta }$, is the integral of the internal moment divided by the product of the Young's modulus and the area moment of inertia:

${\displaystyle \theta (x)={\frac {1}{EI}}\int M(x)\,dx}$

Integrating the angle of rotation obtains the vertical displacement ${\displaystyle \nu }$:

${\displaystyle \nu (x)=\int \theta (x)dx}$.

9.648533212...×10⁴ C mol⁻¹.[212]

This constant has a simple relation to two other physical constants:

${\displaystyle F\,=\,eN_{A}}$

where

e = 1.602176634×10⁻¹⁹ C;[213]

N_A = 6.02214076×10²³ mol⁻¹.[214]

• Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into static friction ("stiction") between non-moving surfaces, and kinetic friction between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as asperities (see Figure 1).
• Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other.[229][230]

• Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces.[231][232][233]

• Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body.
• Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation.[230]

${\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}}$

${\displaystyle {{\mbox{Rate}}_{1} \over {\mbox{Rate}}_{2}}={\sqrt {M_{2} \over M_{1}}}}$,

where:

Rate₁ is the rate of effusion for the first gas. (volume or number of moles per unit time).

Rate₂ is the rate of effusion for the second gas.

M₁ is the molar mass of gas 1

M₂ is the molar mass of gas 2.

${\displaystyle U}$

${\displaystyle U=-{\frac {GMm}{R}},}$

where ${\displaystyle M}$ and ${\displaystyle m}$ are the masses of the two particles, ${\displaystyle R}$ is the distance between them, and ${\displaystyle G}$ is the gravitational constant.[255]

Close to the Earth's surface, the gravitational field is approximately constant, and the gravitational potential energy of an object reduces to

${\displaystyle U=mgh}$

${\displaystyle m}$

${\displaystyle g=GM_{E}/R_{E}^{2}}$

${\displaystyle h}$

${\displaystyle \left({\frac {1^{-1}+4^{-1}+4^{-1}}{3}}\right)^{-1}={\frac {3}{{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{4}}}}={\frac {3}{1.5}}=2\,.}$

${\displaystyle {\ce {pH}}={\ce {p}}K_{{\ce {a}}}+\log _{10}\left({\frac {[{\ce {Base}}]}{[{\ce {Acid}}]}}\right)}$

${\displaystyle PV=nRT}$

where ${\displaystyle P}$, ${\displaystyle V}$ and ${\displaystyle T}$ are the pressure, volume and temperature; ${\displaystyle n}$ is the amount of substance; and ${\displaystyle R}$ is the ideal gas constant. It is the same for all gases.

When any system at equilibrium for a long period of time is subjected to a change in concentration, temperature, volume, or pressure, (1) the system changes to a new equilibrium, and (2) this change partly counteracts the applied change.

It is common to treat the principle as a more general observation of systems,[309] such as

When a settled system is disturbed, it will adjust to diminish the change that has been made to it

or, "roughly stated",[309]

Any change in status quo prompts an opposing reaction in the responding system.

${\displaystyle \lim _{x\to c}f(x)=\lim _{x\to c}g(x)=0{\text{ or }}\pm \infty ,}$

${\displaystyle g'(x)\neq 0}$

${\displaystyle \lim _{x\to c}{\frac {f'(x)}{g'(x)}}}$

${\displaystyle \lim _{x\to c}{\frac {f(x)}{g(x)}}=\lim _{x\to c}{\frac {f'(x)}{g'(x)}}.}$

${\displaystyle \log _{b}(x)=y\ }$ exactly if ${\displaystyle \ b^{y}=x\ }$ and ${\displaystyle \ x>0}$ and ${\displaystyle \ b>0}$ and ${\displaystyle \ b\neq 1}$.

For example, log₂ 64 = 6, as 2⁶ = 64.