formula.expert

Formula solvers — D

0–9 · 1A · 84B · 98C · 181D · 94E · 80F · 66G · 65H · 72I · 46J · 6K · 18L · 63M · 105N · 46O · 21P · 138Q · 4R · 113S · 194T · 104U · 8V · 31W · 51X · 3Y · 6Z · 3

94 of 1701 solvers. Browse by category instead →

D-Value (Decimal Reduction Time)

D=tLRD = \frac{t}{\mathrm{LR}}

Water TreatmentThe decimal reduction time: how long at a fixed temperature it takes to reduce a population by one log — a factor of ten. It is the slope of the straight survival line on semi-log paper, and it is meaningless without the temperature it was measured at, which is why it is always written with one attached, as D₁₂₁.

Daily Light Integral (DLI)

DLI=PPFD×tDLI = PPFD \times t

Indoor & GreenhouseCrop ProductionThe total photosynthetically active photons a crop banks in a day, from the light intensity at the canopy and the length of the photoperiod. The single number that best predicts how an indoor crop will grow.

Daily Water Requirement of a Herd

W=n wW = n \, w

Livestock & FeedThe water a herd drinks in a day, from the head count and the demand per head. Water is the nutrient stock run short of first and the one least often measured.

Damköhler Number (First Order)

Da=k τ\mathrm{Da} = k\,\tau

Chemical EngineeringThe single dimensionless group that decides how far a first-order reaction gets: rate constant times residence time. It compares the speed of the chemistry with the speed of the flow, and once it is fixed the conversion is fixed — whatever the vessel's actual size.

Damped Natural Frequency

fd=fn1−ζ2f_d = f_n \sqrt{1 - \zeta^{2}}

Machine DesignThe frequency a damped system actually rings at, which is always a little below the undamped one. For the damping levels found in real structures the difference is negligible — and knowing exactly how negligible is the useful part.

Damping Ratio from the Damping Coefficient

ζ=c2km\zeta = \frac{c}{2\sqrt{k m}}

Machine DesignThe dashpot's rating measured against the one value that would stop the oscillation dead: ζ = c/c_c, where c_c = 2√(km). The number that decides whether a system rings, creeps back, or does something in between.

Darcy–Weisbach Head Loss

hf=f LD v22gh_f = f \, \frac{L}{D} \, \frac{v^{2}}{2g}

HVAC & HydronicsFluid MechanicsPhysicsThe rigorous pipe friction equation: head loss from friction factor, length-to-diameter ratio and velocity head, with g = 9.80665 m/s².

Darcy's Law for Groundwater Flow

Q=k i AQ = k\,i\,A

Soil MechanicsFluid MechanicsDarcy's law for laminar flow through soil: discharge equals hydraulic conductivity times hydraulic gradient times gross cross-sectional area.

Days Between Softener Regenerations

t=mcapC Qt = \frac{m_{\text{cap}}}{C \, Q}

Water TreatmentChemistryGives the run time a softener achieves between regenerations from its rated hardness capacity, the raw water hardness and the average water usage rate.

De Broglie Wavelength

λ=hmv\lambda = \frac{h}{m v}

Modern PhysicsPhysicsEvery moving particle has a wavelength: Planck's constant over its momentum mv.

Dead Reckoning Position

Δφ=S tcos⁡CR\Delta\varphi = \frac{S\,t\cos C}{R}

Navigation & PositionThe classic DR advance: speed times time gives the distance run, and the cosine of the course splits it into the change of latitude. The oldest position-finding method there is, and still the one that catches an instrument failure.

Deadweight Loss of a Per-Unit Tax

DWL=12 t ΔQ\mathit{DWL} = \tfrac{1}{2}\,t\,\Delta Q

Prices & MarketsValue destroyed by a per-unit tax beyond the revenue it collects: half the tax times the fall in quantity traded. Those are the trades that were worth making, and that the tax stopped.

Deborah Number

De=λtobs\mathrm{De} = \frac{\lambda}{t_{\mathrm{obs}}}

Polymers & Plastics ProcessingA material's relaxation time divided by the time you spend watching it. Below one it flows and you call it a liquid; above one it holds its shape and you call it a solid — and the same material gives both answers depending on how long you look.

Debris Flow Impact Pressure

p=a ρ v2p = a\,\rho\,v^{2}

Soil MechanicsFluid MechanicsHydrodynamic impact pressure of a debris flow on an obstruction, from the bulk density of the mixture and the flow velocity, with an empirical coefficient that carries the whole disagreement in the literature.

Decibel Power Gain

GdB=10log⁡10 ⁣(P2P1)G_{dB} = 10 \log_{10}\!\left(\frac{P_{2}}{P_{1}}\right)

Electrical TradeElectricity & MagnetismGain or loss in decibels between two power levels, the logarithmic ratio used throughout audio, RF and communications work.

Decibel Sound Level

β=10log⁡10 ⁣(II0)\beta = 10 \log_{10}\!\left(\frac{I}{I_0}\right)

Waves & OscillationsPhysicsAcoustics & NoiseSound level in decibels compares an intensity to the threshold of hearing, I₀ = 10⁻¹² W/m².

Decibel Voltage Gain

GdB=20log⁡10 ⁣(V2V1)G_{dB} = 20 \log_{10}\!\left(\frac{V_{2}}{V_{1}}\right)

Electrical TradeElectricity & MagnetismGain or loss in decibels computed from a voltage ratio, which carries a factor of 20 because power varies with the square of voltage.

Declining-Balance Depreciation (Book Value)

B=C (1−d)kB = C\,(1 - d)^k

Money & BusinessBook value of an asset after k years when a fixed fraction d of the remaining value is written off every year.

Decrement Factor from Damping Depth

f=e−x/df = e^{-x/d}

Heat TransferThe fraction of the outdoor temperature swing that still exists at depth x into the material. It falls exponentially with thickness measured in damping depths, so the first few centimetres do most of the work and the last few do almost none. Not to be confused with the logarithmic decrement of a damped vibration, which is an unrelated quantity that happens to share a word.

Decrement Factor from Diffusivity and Period

f=exp⁡ ⁣(−xπαP)f = \exp\!\left(-x\sqrt{\frac{\pi}{\alpha P}}\right)

Heat TransferThe same amplitude ratio as the decrement-factor page, written straight from the material's diffusivity and the length of the cycle so no damping depth has to be computed first. Handy when comparing two materials, or the same material against the daily and the annual swing.

Deep Drawing Force (Swift)

F=πdt UTS(Dd−0.7)F = \pi d t \, UTS \left( \frac{D}{d} - 0.7 \right)

Machining & TurningThe peak force the punch has to pull to draw a flat blank into a cylindrical cup, in the form Swift published in 1952. The circumference of the cup times the thickness times the tensile strength, scaled by how much material has to be dragged in — the term in brackets, whose 0.7 is empirical rather than derived.

Deep-Water Wave Celerity

c0=g T2πc_0 = \frac{g\,T}{2\pi}

Coastal & Ocean WavesHow fast an individual crest travels in deep water, set by the period and nothing else. Long waves outrun short ones, which is why the swell from a distant storm arrives sorted — the longest periods first — and why a rising swell with a lengthening period is the classic warning that weather is coming.

Deep-Water Wave Power per Metre of Crest

P=ρg2H2T64πP = \frac{\rho g^{2} H^{2} T}{64\pi}

Coastal & Ocean WavesThe rate at which a deep-water wave train delivers energy across a line one metre long drawn along the crest. It is the energy density carried at the group velocity, and it is how every marine-energy resource on earth is quoted — because a wave front has no width of its own, so the resource has to be stated per metre of it.

Deep-Water Wavelength from Period

L0=g T22πL_0 = \frac{g\,T^{2}}{2\pi}

Coastal & Ocean WavesIn water deeper than half a wavelength, a wave's length is fixed by its period alone — nothing about the wind that made it, the depth beneath it or how big it is enters. This is the first number to compute about any sea state, because it is the length every other coastal criterion is measured against.

Defects Per Million Opportunities (DPMO)

DPMO=DU×O×106\mathit{DPMO} = \frac{D}{U \times O} \times 10^{6}

Industrial EngineeringDefect rate on a scale that makes very good processes comparable: defects found, divided by the units inspected times the chances to go wrong on each unit, scaled to a million.

Degree of Saturation

x=qcx = \frac{q}{c}

Traffic Flow & SignalsDemand divided by capacity for one movement at a signal. It is the single number that says whether a timing plan works, and it is the term that makes every delay equation run away as it approaches one.

Degree of Saturation (Moist Air)

μ=WWs\mu = \frac{W}{W_s}

HVAC & HydronicsThermodynamicsThe humidity ratio present divided by the humidity ratio at saturation for the same temperature and pressure — close to relative humidity but not equal to it, and the quantity older charts plot as percentage saturation.

Degree of Saturation (Se = wGs)

S=w GseS = \frac{w\,G_s}{e}

Soil MechanicsStrength of MaterialsDegree of saturation from water content, specific gravity of solids and void ratio, using the phase identity Se = wGs.

Degrees of Freedom (One-Sample t)

df=n−1df = n - 1

StatisticsAlgebraThe degrees of freedom used to look up a critical value for a one-sample t-test or confidence interval, one fewer than the sample size.

Degrees of Superheat

ΔTsh=T−Ts(p)\Delta T_{sh} = T - T_s(p)

ThermodynamicsWater TreatmentHVAC & HydronicsHow many degrees a steam temperature sits above saturation at its own pressure, with the saturation temperature taken from IAPWS-IF97 Region 4.

Delta Line and Phase Current

IL=3 IφI_{L} = \sqrt{3} \, I_{\varphi}

Electrical TradeElectricity & MagnetismIn a delta connection the line current is √3 times the current in each winding, while line and phase voltages are equal.

Delta to Wye Resistance Transformation

RA=RabRcaRab+Rbc+RcaR_{A} = \frac{R_{ab} R_{ca}}{R_{ab} + R_{bc} + R_{ca}}

Electricity & MagnetismElectrical TradeThe wye arm at node A that behaves identically to a delta of three resistors: the product of the two delta legs touching A over the sum of all three.

Dennard Scaling and Power Density

Pnew′′Pold′′=(κν)2\frac{P''_{new}}{P''_{old}} = \left(\frac{\kappa}{\nu}\right)^2

Semiconductors & ChipsHow power per unit of chip area changes when dimensions shrink by κ but supply voltage only shrinks by ν. Dennard's 1974 rules had the two equal, and power density stayed constant. When ν fell behind κ, it stopped.

Density

ρ=mV\rho = \tfrac{m}{V}

PhysicsChemistryWater TreatmentMass per unit volume.

Departure of a Traverse Leg

Dep=Lsin⁡α\text{Dep} = L\sin\alpha

Civil & SurveyingTrigonometryEast-west component of a traverse course, taken from the measured horizontal distance and the azimuth of the line.

Depth-Limited Breaking Wave Height

Hb=γb dbH_b = \gamma_b\, d_b

Coastal & Ocean WavesA wave running up a beach breaks when its height reaches a fixed fraction of the water depth. The fraction is near 0.78 for a solitary wave on a flat bottom — McCowan's classical result — and it is why the surf zone has an outer edge you can see, and why the wave that reaches a structure is often limited by the water in front of it rather than by the storm offshore.

Derated Conductor Ampacity

Ia=It CT CBI_{a} = I_{t} \, C_{T} \, C_{B}

Electrical TradeAmpacity left after the two corrections that always apply: ambient temperature and the number of current-carrying conductors bundled together.

Design Lane ESALs

w18=DD DL W18w_{18} = D_D \, D_L \, W_{18}

Axle Loads & PavementThe share of a highway's total equivalent single axle loads that lands in the one lane the pavement is designed for, after splitting the two-way total by direction and then by lane. Pavement is designed for the worst lane, not the average one.

Destination Latitude from Course and Distance

φ2=arcsin⁡(sin⁡φ1cos⁡dR+cos⁡φ1sin⁡dRcos⁡θ)\varphi_2 = \arcsin\left(\sin\varphi_1\cos\frac{d}{R} + \cos\varphi_1\sin\frac{d}{R}\cos\theta\right)

Navigation & PositionWhere a great circle course of a given length puts you: the latitude reached from a starting latitude, an initial true bearing and a distance run. The answer carries the change of longitude with it.

Desuperheater Water Injection Rate

m˙w=m˙1 h1−h2h2−hw\dot{m}_w = \dot{m}_1 \, \frac{h_1 - h_2}{h_2 - h_w}

ThermodynamicsWater TreatmentHVAC & HydronicsSpray water a desuperheater needs to bring superheated steam down to a target enthalpy, straight from the mass and energy balance across the station.

Detention Storage from a Routing Step

ΔS=(Qin−Qout) Δt\Delta S = (Q_{in} - Q_{out}) \, \Delta t

Water & WastewaterCivil & SurveyingFluid MechanicsOne step of the reservoir continuity equation: the storage a detention basin accumulates is the difference between inflow and outflow multiplied by the length of the step.

Determinant of a 2×2 Matrix

D=ad−bcD = ad - bc

Vectors & MatricesAlgebraComputes the determinant of a two-by-two matrix as the difference of its diagonal products, the number that decides invertibility.

Determinant of a 3×3 Matrix

D=a11(a22a33−a23a32)−a12(a21a33−a23a31)+a13(a21a32−a22a31)D = a_{11}(a_{22}a_{33} - a_{23}a_{32}) - a_{12}(a_{21}a_{33} - a_{23}a_{31}) + a_{13}(a_{21}a_{32} - a_{22}a_{31})

Vectors & MatricesAlgebraComputes the determinant of a three-by-three matrix by cofactor expansion along the first row, using all nine entries.

Deterministic Queue at the End of Red

Q=q rQ = q\,r

Traffic Flow & SignalsVehicles arrive at a steady rate and none leave while the light is red, so the queue at the moment the green comes on is simply the arrival rate multiplied by the red. It is the crudest queue model there is, and it is the one that decides how long a turn bay has to be.

Dew Point (Magnus Approximation)

Td=c γb−γ,γ=ln⁡ ⁣RH100+b Tc+TT_d = \frac{c\,\gamma}{b - \gamma}, \quad \gamma = \ln\!\frac{\mathrm{RH}}{100} + \frac{b\,T}{c + T}

Everyday & HealthThermodynamicsDew point from air temperature and relative humidity by the Magnus formula with the WMO's Sonntag coefficients (b = 17.62, c = 243.12 °C).

Dew Point from Humidity Ratio

Td=243.04 γ17.625−γ,γ=ln⁡ ⁣pv610.94,pv=W p0.62198+WT_d = \frac{243.04\,\gamma}{17.625 - \gamma}, \quad \gamma = \ln\!\frac{p_v}{610.94}, \quad p_v = \frac{W\,p}{0.62198 + W}

HVAC & HydronicsThermodynamicsAir Quality & DispersionThe temperature at which air of a given humidity ratio and barometric pressure starts to condense, by running the vapour-pressure chain backwards through the Magnus fit.

Die Yield from Defect Density (Poisson Model)

Y=e−D0AY = e^{-D_0 A}

Semiconductors & ChipsFraction of dies with no fatal defect, when defects fall randomly on the wafer at a known density. Because the area sits in an exponent, doubling the die size does far worse than halving the yield.

Differential Levelling Elevation

E2=E1+BS−FSE_2 = E_1 + \text{BS} - \text{FS}

Civil & SurveyingCarries an elevation forward one instrument setup, adding the backsight to the known point and subtracting the foresight.

Diffraction Grating Equation

mλ=dsin⁡θm \lambda = d \sin\theta

OpticsWaves & OscillationsPhysicsBright beams leave a grating at angles where the path difference d sin θ is a whole number of wavelengths.

Diffraction-Limited Spot Diameter (Airy Disc)

d=2.44 λfDd = \frac{2.44 \, \lambda f}{D}

OpticsThe diameter of the central bright disc — first dark ring to first dark ring — that a round aperture of diameter D produces at the focus of a lens of focal length f. Airy worked out the pattern in 1835 and it is still the floor under every imaging and focusing system: no lens, however perfect, focuses tighter than its own aperture allows.

Dilution Equation (C1V1 = C2V2)

C1V1=C2V2C_1 V_1 = C_2 V_2

ChemistryWater TreatmentStates that concentration times volume is conserved when a solution is diluted, since the moles of solute do not change.

Dilution to a Target Gravity

V2=V1P1P2V_2 = \frac{V_1 P_1}{P_2}

Brewing & FermentationThe volume a wort reaches once it is diluted to a lower gravity, worked in gravity points. The fix for a batch that came out stronger than the recipe asked for.

DIM Divisor as a Density

ρdim=mbd Vb\rho_{\mathrm{dim}} = \frac{m_b}{d \, V_b}

Freight & ShippingA dimensional-weight divisor is a specific volume in disguise — so many cubic inches per pound, or cubic centimetres per kilogram. Turn it over and it becomes a density you can compare with your own freight. Declare the basis and this page does the turning.

Dimensional Weight

Wdim=V ρdimW_{\mathrm{dim}} = V \, \rho_{\mathrm{dim}}

Freight & ShippingThe weight a carrier assigns to a package because of the space it occupies rather than the mass it has. Written the honest way — as a volume multiplied by a density the carrier has chosen — instead of as a volume divided by a mystery number.

Direct Count from Mass and Length — Tex, Decitex and Denier

ρL=mL\rho_L = \frac{m}{L}

Textiles & FabricThe whole of the direct count system in one division: weigh a measured length of yarn and divide. Tex is the grams in 1000 m, decitex the grams in 10 000 m, denier the grams in 9000 m — three names for one measurement made against three reference lengths, which is why denier = 9 × tex and dtex = 10 × tex exactly.

Direction Angle of a 2D Vector

θ=atan2⁡(vy,  vx)\theta = \operatorname{atan2}(v_y,\; v_x)

Vectors & MatricesTrigonometryAlgebraGives the direction a two-dimensional vector points, measured counterclockwise from the positive x-axis, from its two components.

Disc Clutch Torque (Uniform Wear)

T=Nπμpari(ro2−ri2)T = N \pi \mu p_{a} r_{i} \left( r_{o}^{2} - r_{i}^{2} \right)

Machine DesignThe torque an annular disc clutch transmits on the uniform-wear assumption, where the pressure is highest at the INNER radius and the product p·r is constant. The conservative and standard basis for clutch and disc-brake design.

Discount Price (Percentage Off)

S=L (1−d)S = L\,(1 - d)

Money & BusinessPrice after a percentage is taken off the list price, and the discount implied by any pair of list and sale prices.

Discriminant of a Quadratic

Δ=b2−4ac\Delta = b^2 - 4ac

AlgebraThe quantity b² − 4ac under the square root, which reveals how many real roots a quadratic has before you solve it.

Displacement (Uniform Acceleration)

d=v0t+12at2d = v_0 t + \tfrac{1}{2} a t^2

MechanicsPhysicsDistance travelled under constant acceleration, starting from an initial velocity, over a time t.

Displacement from Average Velocity

d=v0+v2 td = \frac{v_0 + v}{2} \, t

MechanicsPhysicsDisplacement as the average of initial and final velocities multiplied by the elapsed time, valid for uniform acceleration.

Displacement from Final Velocity (d = vt − ½at²)

d=vt−12at2d = v t - \tfrac{1}{2} a t^2

MechanicsPhysicsThe fifth kinematic equation: displacement from the FINAL velocity and the time, for when the starting speed is the unknown.

Dissolved Oxygen Saturation with Temperature

ln⁡Cs=−139.34411+1.575701×105T−6.642308×107T2+1.243800×1010T3−8.621949×1011T4\ln C_s = -139.34411 + \frac{1.575701 \times 10^5}{T} - \frac{6.642308 \times 10^7}{T^2} + \frac{1.243800 \times 10^{10}}{T^3} - \frac{8.621949 \times 10^{11}}{T^4}

Corrosion & ProtectionHow much oxygen fresh water can hold at saturation, falling from about 14.6 mg/L at freezing to 7.6 at 30 °C. The Benson and Krause fit adopted by Standard Methods, and the reason deaerators and hot systems corrode differently from cold ones.

Distance Attenuation from a Point Source

L2=L1−20log⁡10 ⁣(r2r1)L_2 = L_1 - 20\log_{10}\!\left(\frac{r_2}{r_1}\right)

Acoustics & NoiseMove twice as far from a point source in the open and the level drops 6 dB — every time, regardless of the starting level. Ten times the distance is 20 dB. This is the cheapest noise control there is, when there is room for it.

Distance Formula (2D)

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

GeometryAlgebraStraight-line distance between two points in the coordinate plane.

Distance Formula (3D)

d=Δx2+Δy2+Δz2d = \sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2}

AlgebraStraight-line distance between two points from their separations along each axis.

Distance from a Point to a Line

d=∣Ax0+By0+C∣A2+B2d = \frac{\left| A x_0 + B y_0 + C \right|}{\sqrt{A^2 + B^2}}

AlgebraGeometryPerpendicular distance from a point to a line written in general form Ax + By + C = 0, the shortest gap between the two.

Distance to the Visible Horizon

D=h(2R+h)D = \sqrt{h\left(2R + h\right)}

Navigation & PositionHow far away the sea horizon is from a given height of eye: the tangent line from the observer to the sphere. The geometric figure, before atmospheric refraction pushes it out by about a tenth.

Distribution Uniformity

DU=dˉlqdˉDU = \frac{\bar{d}_{lq}}{\bar{d}}

Crop ProductionHow evenly an irrigation system puts water on the ground: the average depth caught in the driest quarter of the field, divided by the average depth over the whole of it. The number a catch-can test exists to produce.

Dittus-Boelter Correlation

Nu=0.023 Re0.8 Prn\mathrm{Nu} = 0.023 \, \mathrm{Re}^{0.8} \, \mathrm{Pr}^{n}

Heat TransferFluid MechanicsTurbulent tube-flow Nusselt number, valid for Re above 10,000, Pr from 0.6 to 160 and L/D over 10, with n = 0.4 heating and 0.3 cooling.

Divisor Count from Prime Exponents

d(n)=(a1+1)(a2+1)(a3+1)d(n) = (a_1 + 1)(a_2 + 1)(a_3 + 1)

AlgebraHow many divisors a number has, read straight off its prime exponents: add one to each and multiply. A number with three or fewer distinct primes; set an unused exponent to 1.

Doppler Effect (Approaching Observer)

f′=f(v+vo)vf' = \frac{f (v + v_o)}{v}

Waves & OscillationsPhysicsA listener moving toward a stationary source meets wavefronts more often and hears a higher frequency.

Doppler Effect (Approaching Source)

f′=fvv−vsf' = \frac{f v}{v - v_s}

Waves & OscillationsPhysicsObserved frequency rises when a sound source approaches, as each wavefront is emitted closer to the listener.

Dose Achieved from Chemical Added

C=mV ρwC = \frac{m}{V \, \rho_w}

Water TreatmentChemistryConcentration reached in a system of known volume after adding a measured mass of chemical, at 8.34 lb of water per US gallon.

Dot Product from Magnitudes and Included Angle

a⃗⋅b⃗=∣a⃗∣ ∣b⃗∣cos⁡θ\vec{a}\cdot\vec{b} = |\vec{a}|\,|\vec{b}|\cos\theta

Vectors & MatricesTrigonometryPhysicsGives the scalar product of two vectors from their lengths and the angle between them, the geometric face of the dot product.

Dot Product of Two 2D Vectors (Components)

a⃗⋅b⃗=axbx+ayby\vec{a}\cdot\vec{b} = a_x b_x + a_y b_y

Vectors & MatricesAlgebraMultiplies two plane vectors component by component and adds the results, giving the scalar that measures how much they share a direction.

Dot Product of Two 3D Vectors (Components)

a⃗⋅b⃗=axbx+ayby+azbz\vec{a}\cdot\vec{b} = a_x b_x + a_y b_y + a_z b_z

Vectors & MatricesAlgebraMultiplies two space vectors component by component and sums the three products, the standard test for perpendicularity in three dimensions.

Double-Slit Fringe Spacing

Δy=λLd\Delta y = \frac{\lambda L}{d}

OpticsWaves & OscillationsPhysicsSpacing between adjacent bright fringes on a screen a distance L behind two slits d apart.

Doubling Time from Specific Growth Rate

td=ln⁡2μt_d = \frac{\ln 2}{\mu}

Chemical EngineeringThe bridge between the number an engineer calculates with and the number a microbiologist says out loud. µ is a reciprocal time and comes out of every rate balance; the doubling time is what somebody at the bench quotes. They are the same fact, natural-log-of-two apart.

Drag Equation from the Drag Coefficient

D=q S CDD = q \, S \, C_D

Aerospace & FlightThe drag on an aircraft written the way an aerodynamicist writes it: dynamic pressure times the SAME wing reference area used for lift, times the drag coefficient. Not the frontal area a car's drag is built on.

Drag Force (F = ½CdρAv²)

FD=12CdρAv2F_D = \tfrac{1}{2} C_d \rho A v^{2}

MechanicsPhysicsAerodynamic drag on a body moving through a fluid, growing with the square of speed and with frontal area and density.

Drag Polar

CD=CD0+CDiC_D = C_{D0} + C_{Di}

Aerospace & FlightThe whole drag of an aircraft split in two: a part that is there whatever the wing is doing, and a part that is the price of lift. Every performance calculation an aircraft ever needs starts from this sum.

Drain Line Fall from Slope and Run

F=SLF = S L

Trades & ConstructionThe vertical drop a drain gains over a measured run, from a slope quoted as a plain ratio such as 1:40 or a quarter inch per foot.

Drawbar Power

P=F vP = F \, v

Farm OperationsThe power a tractor delivers through the drawbar: draft force times travel speed. The figure that decides whether a tractor can pull an implement at the speed the job needs.

Driven Rod Resistance to Earth

R=ρ2πL[ln⁡ ⁣(4La)−1]R = \frac{\rho}{2\pi L} \left[ \ln\!\left( \frac{4L}{a} \right) - 1 \right]

Electrical TradeResistance to earth of a single rod driven vertically into uniform soil, from the soil's resistivity and the rod's length and radius.

Drop Height of a Horizontally Launched Projectile

y=12gt2y = \tfrac{1}{2} g t^{2}

MechanicsPhysicsDistance a horizontally launched projectile falls in a given time, independent of how fast it was thrown sideways.

Drug Half-Life from Clearance and Volume of Distribution

t1/2=ln⁡2⋅VdCLt_{1/2} = \frac{\ln 2 \cdot V_d}{\mathrm{CL}}

Biomedical & ClinicalElimination half-life for a one-compartment drug: the time to fall by half, set entirely by the volume of distribution and the clearance.

Dry Matter Intake from Body Weight

DMI=p×BWDMI = p \times BW

Livestock & FeedDaily dry matter intake estimated as a percentage of body weight — the first figure in any ration, and the one that sets how much of everything else the animal can physically consume.

Dry Matter Yield

Ydm=Yf DMY_{dm} = Y_f \, DM

Crop ProductionThe dry matter in a fresh-weight harvest. Forage and silage are bought, budgeted and fed on dry matter, because the water in a wet crop is worth nothing and weighs a great deal.

Dry Product per Tank

m=R Am = R \, A

Crop ProductionHow much dry product to weigh into one tank: the label's rate per unit area times the area that tank will cover.

Dry Unit Weight from Gs and Void Ratio

γd=Gs γw1+e\gamma_d = \frac{G_s\,\gamma_w}{1 + e}

Soil MechanicsStrength of MaterialsDry unit weight of a soil from the specific gravity of its solids and its void ratio, the phase-diagram route used to back out e in the lab.

Dry Unit Weight from Moist Unit Weight

γd=γ1+w100\gamma_d = \frac{\gamma}{1 + \dfrac{w}{100}}

Soil MechanicsStrength of MaterialsStrips the pore water out of a measured bulk unit weight to give the dry unit weight used for compaction control and phase work.

Dwight's Equation for Anode Resistance to Earth

R=ρ2πL[ln⁡ ⁣(8Ld)−1]R = \frac{\rho}{2 \pi L} \left[ \ln\!\left(\frac{8L}{d}\right) - 1 \right]

Corrosion & ProtectionH. B. Dwight's 1936 result for a vertical rod in uniform soil: the resistance between a buried anode and remote earth, from the soil resistivity and the anode's length and diameter. Almost the whole resistance of a cathodic protection circuit.

Dynamic Pressure (q = ½ρv²)

q=12ρv2q = \tfrac{1}{2} \rho v^{2}

Fluid MechanicsPhysicsThe kinetic energy per unit volume of a moving fluid — the pressure of motion itself.