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Fluid Mechanics formula solvers

Volumetric Flow Rate (Q = Av)

Q=AvQ = A v

Fluid MechanicsWater TreatmentPhysicsFlow through a duct or pipe: cross-sectional area times average flow velocity.

Continuity Equation (A₁v₁ = A₂v₂)

A1v1=A2v2A_1 v_1 = A_2 v_2

Fluid MechanicsWater TreatmentPhysicsFor incompressible flow, the same volume per second passes every cross-section of the pipe.

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.

Buoyant Force (Archimedes' Principle)

Fb=ρVgF_b = \rho V g

Fluid MechanicsPhysicsThe upward force on a submerged body equals the weight of the fluid it displaces, with g = 9.80665 m/s².

Torricelli's Law (v = √(2gh))

v=2ghv = \sqrt{2 g h}

Fluid MechanicsWater TreatmentPhysicsSpeed of fluid jetting from an opening a depth h below the free surface, with g = 9.80665 m/s².

Pressure Head (h = P/ρg)

h=Pρgh = \frac{P}{\rho g}

Fluid MechanicsWater TreatmentPhysicsConverts a pressure into the equivalent height of a fluid column, with g = 9.80665 m/s².

Velocity Head (h = v²/2g)

hv=v22gh_v = \frac{v^{2}}{2g}

Fluid MechanicsWater TreatmentPhysicsThe kinetic energy of a flow expressed as an equivalent column height, with g = 9.80665 m/s².

Reynolds Number

Re=ρvDμRe = \frac{\rho v D}{\mu}

Fluid MechanicsPhysicsThe dimensionless ratio of inertial to viscous forces that decides laminar versus turbulent flow.

Poiseuille's Law

Q=π ΔP r48μLQ = \frac{\pi \, \Delta P \, r^{4}}{8 \mu L}

Fluid MechanicsPhysicsLaminar flow rate through a round pipe — proportional to the fourth power of the radius.

Stokes' Drag (F = 6πμrv)

F=6πμrvF = 6\pi \mu r v

Fluid MechanicsPhysicsViscous drag on a small sphere creeping through a fluid at low Reynolds number.

Specific Gravity

SG=ρρwaterSG = \frac{\rho}{\rho_{water}}

Fluid MechanicsWater TreatmentChemistryDensity expressed as a multiple of water's 1000 kg/m³.

Hydraulic Power (P = ρgQh)

P=ρgQhP = \rho g Q h

Fluid MechanicsWater TreatmentPhysicsPower needed to lift a flow Q through a head h, with g = 9.80665 m/s².

Gauge and Absolute Pressure

Pabs=Pgauge+PatmP_{abs} = P_{gauge} + P_{atm}

Fluid MechanicsThermodynamicsPhysicsAbsolute pressure is the gauge reading plus the surrounding atmospheric pressure.

Hydronic Heat Transfer (Water)

Q˙=ρwcwV˙ ΔT\dot{Q} = \rho_w c_w \dot{V} \, \Delta T

HVAC & HydronicsThermodynamicsFluid MechanicsHeat carried by a water loop from flow rate and supply-to-return ΔT — the SI form of the trade rule BTU/hr = 500 × GPM × ΔT.

Condenser Water Flow Rate

V˙=Q˙⋅HRFρwcw ΔT\dot{V} = \frac{\dot{Q} \cdot \mathrm{HRF}}{\rho_w c_w \, \Delta T}

HVAC & HydronicsFluid MechanicsWater TreatmentTower water flow needed to reject a chiller's load plus compressor heat, the physics behind the 3 gpm per ton at 10 °F rule of thumb.

Round Duct Air Velocity

v=4V˙πd2v = \frac{4 \dot{V}}{\pi d^{2}}

HVAC & HydronicsFluid MechanicsAir velocity in a round duct from the volume flow and the duct diameter, the check that keeps branches quiet and mains efficient.

Equivalent Round Duct Diameter

De=1.30(ab)0.625(a+b)0.25D_e = 1.30 \frac{(ab)^{0.625}}{(a+b)^{0.25}}

HVAC & HydronicsFluid MechanicsHuebscher's equation for the round duct that has the same friction loss and airflow as a given rectangular duct of sides a and b.

Air Changes per Hour (ACH)

ACH=3600 V˙Vroom\mathrm{ACH} = \frac{3600 \, \dot{V}}{V_{room}}

HVAC & HydronicsFluid MechanicsHow many times per hour a ventilation rate replaces the air in a room, the ventilation yardstick behind BTU/hr = 60 × CFM ÷ room volume.

Expansion Tank Acceptance Volume

Vt=Vs e1−P1P2V_t = \frac{V_s \, e}{1 - \dfrac{P_1}{P_2}}

HVAC & HydronicsFluid MechanicsDiaphragm expansion tank size for a closed hydronic loop from system volume, water expansion and the absolute fill and relief pressures.

Loop Water Expansion Volume

ΔV=V0 β ΔT\Delta V = V_0 \, \beta \, \Delta T

HVAC & HydronicsFluid MechanicsThermodynamicsVolume a hydronic loop's water gains when heated, from the starting volume, the volumetric expansion coefficient and the temperature rise.

Hydronic Static Fill Pressure

P=ρwgH+PmarginP = \rho_w g H + P_{margin}

HVAC & HydronicsFluid MechanicsCold fill pressure a closed loop needs to lift water to its highest point plus a safety margin, the SI form of the 2.31 ft per psi rule.

Pump Affinity Law — Flow vs Speed

Q2Q1=N2N1\frac{Q_2}{Q_1} = \frac{N_2}{N_1}

HVAC & HydronicsFluid MechanicsWater TreatmentFirst affinity law: a centrifugal pump's capacity changes in direct proportion to shaft speed when the impeller diameter is unchanged.

Pump Affinity Law — Head vs Speed

H2H1=(N2N1)2\frac{H_2}{H_1} = \left(\frac{N_2}{N_1}\right)^{2}

HVAC & HydronicsFluid MechanicsWater TreatmentSecond affinity law: pump head varies with the square of shaft speed, so a 20% speed cut costs 36% of the developed head.

Pump Affinity Law — Power vs Speed

P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}

HVAC & HydronicsFluid MechanicsWater TreatmentThird affinity law: absorbed power varies with the cube of shaft speed — the single relation that pays for every variable-frequency drive.

Pump Affinity Law — Flow vs Impeller Diameter

Q2Q1=D2D1\frac{Q_2}{Q_1} = \frac{D_2}{D_1}

HVAC & HydronicsFluid MechanicsWater TreatmentCapacity scales directly with trimmed impeller diameter at constant speed, the classic way to de-rate an oversized centrifugal pump permanently.

Pump Affinity Law — Head vs Impeller Diameter

H2H1=(D2D1)2\frac{H_2}{H_1} = \left(\frac{D_2}{D_1}\right)^{2}

HVAC & HydronicsFluid MechanicsWater TreatmentDeveloped head falls with the square of the trimmed impeller diameter, so a 10% trim sheds about 19% of the head at constant speed.

Fan Affinity Law — Airflow vs Speed

Q2Q1=N2N1\frac{Q_2}{Q_1} = \frac{N_2}{N_1}

HVAC & HydronicsFluid MechanicsPhysicsFan airflow in CFM changes in direct proportion to wheel speed, the first law used when re-sheaving a belt-driven air handler.

Fan Affinity Law — Static Pressure vs Speed

SP2SP1=(N2N1)2\frac{SP_2}{SP_1} = \left(\frac{N_2}{N_1}\right)^{2}

HVAC & HydronicsFluid MechanicsPhysicsFan static pressure rises with the square of wheel speed, the reason a modest re-sheave can overpressurise ductwork and blow out flex connections.

Fan Affinity Law — Power vs Speed

P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}

HVAC & HydronicsFluid MechanicsPhysicsFan brake power varies with the cube of wheel speed — the law behind variable-air-volume energy savings and behind burnt-out re-sheaved motors.

Pump Water Horsepower

WHP=Q H SG3960WHP = \frac{Q \, H \, SG}{3960}

HVAC & HydronicsFluid MechanicsWater TreatmentUseful power delivered to the liquid; the 3960 divisor assumes US gallons per minute, feet of head and horsepower output.

Pump Brake Horsepower

BHP=Q H SG3960 ηBHP = \frac{Q \, H \, SG}{3960 \, \eta}

HVAC & HydronicsFluid MechanicsWater TreatmentShaft power the motor must actually supply; the 3960 constant assumes gpm, feet of head and horsepower, with efficiency as a fraction.

Pump Efficiency from Hydraulic and Shaft Power

η=PhydPshaft\eta = \frac{P_{hyd}}{P_{shaft}}

HVAC & HydronicsFluid MechanicsWater TreatmentPump efficiency is the ratio of hydraulic power delivered to the liquid over the mechanical power absorbed at the shaft.

Fan Brake Horsepower

BHP=Q⋅SP6356 ηBHP = \frac{Q \cdot SP}{6356 \, \eta}

HVAC & HydronicsFluid MechanicsPhysicsShaft power a fan absorbs; the 6356 divisor assumes cubic feet per minute, inches of water gauge and horsepower at the given efficiency.

Total Dynamic Head

TDH=hs+hf+hvTDH = h_s + h_f + h_v

HVAC & HydronicsFluid MechanicsWater TreatmentThe head a pump must develop: static lift plus friction losses plus velocity head, all expressed in feet or metres of the pumped liquid.

Net Positive Suction Head Available (NPSHa)

NPSHa=hatm+hs−hf−hvpNPSH_a = h_{atm} + h_s - h_f - h_{vp}

HVAC & HydronicsFluid MechanicsWater TreatmentAbsolute head available at the pump suction above the liquid's vapour pressure — the margin that keeps a pump from cavitating.

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.

Laminar Friction Factor (f = 64/Re)

f=64Ref = \frac{64}{Re}

HVAC & HydronicsFluid MechanicsPhysicsIn laminar pipe flow the Darcy friction factor depends only on Reynolds number — roughness plays no part below about Re = 2300.

Swamee–Jain Friction Factor

f=0.25[log⁡10 ⁣(ε3.7D+5.74Re0.9)]2f = \frac{0.25}{\left[\log_{10}\!\left(\frac{\varepsilon}{3.7D} + \frac{5.74}{Re^{0.9}}\right)\right]^{2}}

HVAC & HydronicsFluid MechanicsPhysicsAn explicit turbulent friction factor within about 1% of the implicit Colebrook–White equation, valid for Re from 5000 to 10⁸.

Hazen–Williams Head Loss

hf=10.67 L Q1.852C1.852D4.8704h_f = \frac{10.67 \, L \, Q^{1.852}}{C^{1.852} D^{4.8704}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe waterworks head-loss equation in SI form, with Q in m³/s and D in m; the 10.67 constant is 4.727 when working in feet and cubic feet per second.

Hazen–Williams Velocity

v=0.849 C R0.63S0.54v = 0.849 \, C \, R^{0.63} S^{0.54}

HVAC & HydronicsFluid MechanicsWater TreatmentMean water velocity from hydraulic radius and hydraulic gradient; the 0.849 SI constant becomes 1.318 when R is in feet and v in feet per second.

Minor Loss from K Factor

hL=K v22gh_L = K \, \frac{v^{2}}{2g}

HVAC & HydronicsFluid MechanicsWater TreatmentHead lost through a valve or fitting as a multiple of velocity head, with g = 9.80665 m/s² and K taken from a fitting table.

Equivalent Length of a Fitting

Leq=KDfL_{eq} = \frac{K D}{f}

HVAC & HydronicsFluid MechanicsWater TreatmentConverts a fitting's K factor into the length of straight pipe that would cause the same friction loss at the same friction factor.

Valve Flow Coefficient (Cv)

Q=CvΔPSGQ = C_v \sqrt{\frac{\Delta P}{SG}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe US valve-sizing relation: Cv is the gpm of 60 °F water a valve passes at 1 psi drop, so Q is in gpm and ΔP in psi.

Valve Flow Coefficient (Kv, metric)

Q=KvΔpSGQ = K_v \sqrt{\frac{\Delta p}{SG}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe metric valve-sizing relation: Kv is the m³/h of water a valve passes at 1 bar drop, related to Cv by Cv ≈ 1.156 Kv.

Pipe Internal Volume

V=πD24LV = \frac{\pi D^{2}}{4} L

HVAC & HydronicsFluid MechanicsWater TreatmentThe liquid a run of pipe holds, from inside diameter and developed length — the starting point for every flush, fill or chemical dose.

Partially Filled Horizontal Cylindrical Tank

V=L[r2cos⁡−1 ⁣(r−hr)−(r−h)2rh−h2]V = L \left[ r^{2} \cos^{-1}\!\left(\frac{r-h}{r}\right) - (r-h)\sqrt{2rh - h^{2}} \right]

HVAC & HydronicsFluid MechanicsGeometryLiquid volume in a horizontal cylinder from the wetted depth, using the circular segment area times the tank length.

Pipe Velocity from Flow and Diameter

v=4QπD2v = \frac{4Q}{\pi D^{2}}

HVAC & HydronicsFluid MechanicsWater TreatmentAverage velocity in a full round pipe from volumetric flow and inside diameter — the first check on any piping design.

Barlow's Formula (Pipe Pressure Rating)

P=2StDP = \frac{2 S t}{D}

HVAC & HydronicsFluid MechanicsMechanicsInternal pressure a pipe can hold from wall stress, wall thickness and outside diameter — the thin-wall hoop-stress relation used by pipeline codes.

Expansion Loop Leg Length (Guided Cantilever)

L=3ED ΔSaL = \sqrt{\frac{3 E D \, \Delta}{S_a}}

HVAC & HydronicsFluid MechanicsMechanicsLeg length an expansion loop or offset needs to absorb a given thermal movement without exceeding the pipe's allowable stress.

Water Hammer Surge (Joukowsky Equation)

ΔP=ρ a Δv\Delta P = \rho \, a \, \Delta v

HVAC & HydronicsFluid MechanicsPhysicsPeak pressure surge from a sudden change in flow velocity: fluid density times pressure-wave celerity times the velocity change.

Pump Specific Speed (Ns)

Ns=NQH0.75N_s = \frac{N \sqrt{Q}}{H^{0.75}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe dimensional index that classifies impeller type, evaluated in US units with N in rpm, Q in gpm and H in feet at the best efficiency point.

Cycles of Concentration (COC = M/B)

COC=MB\text{COC} = \frac{M}{B}

Water TreatmentFluid MechanicsCycles of concentration for a cooling tower from the makeup and blowdown flows — the master number every treatment program is built around.

Cooling Tower Evaporation Rate

E=0.001 R ΔTE = 0.001 \, R \, \Delta T

Water TreatmentFluid MechanicsThermodynamicsEvaporation loss from a cooling tower using the industry rule of 0.1% of recirculation per degree Fahrenheit of range.

Blowdown Rate from Cycles

B=ECOC−1B = \frac{E}{\text{COC} - 1}

Water TreatmentFluid MechanicsBlowdown a cooling tower must bleed to hold a target cycles of concentration, given its evaporation rate.

Cooling Tower Makeup Water Rate

M=E+B+DM = E + B + D

Water TreatmentFluid MechanicsTotal makeup water a cooling tower needs: the sum of evaporation, blowdown to drain, and drift carried out in the air stream.

Cooling Tower Drift Loss

D=d100 RD = \frac{d}{100} \, R

Water TreatmentFluid MechanicsDrift (windage) loss from a cooling tower as a percentage of the recirculation rate, the fraction of basin water blown out as droplets.

Percent Blowdown

%B=BM×100\%B = \frac{B}{M} \times 100

Water TreatmentFluid MechanicsBlowdown expressed as a percentage of makeup water — the share of purchased water that goes straight to the sewer.

Cooling Tower Heat Rejection

Q=500 R ΔTQ = 500 \, R \, \Delta T

Water TreatmentThermodynamicsFluid MechanicsHeat a cooling tower rejects from flow and range using the trade constant 500 = 8.34 lb/gal × 60 min/h × 1 BTU/(lb·°F).

System Volume from Turnover Time

V=R tV = R \, t

Water TreatmentFluid MechanicsSystem water volume estimated from the recirculation rate and the measured turnover time — the field method when no drawings exist.

Volume of Water Over a Period

V=Q tV = Q \, t

Water TreatmentFluid MechanicsWater a flow delivers over a period — the step that turns a makeup or blowdown rate into the daily or annual volume a customer is billed for.

Chemical-Consuming Loss Rate

L=B+DL = B + D

Water TreatmentChemistryFluid MechanicsFlow that actually carries treatment out of a cooling tower — blowdown plus drift, because evaporation leaves every molecule of inhibitor behind.

Cost of Water Over a Period

Cw=V pwC_w = V \, p_w

Water TreatmentFluid MechanicsWater & WastewaterCost of the water a system buys over a period: the metered volume times the utility's rate, in whatever currency that rate was in.

Sewer Credit for Evaporated Water

Cc=Ve psC_c = V_e \, p_s

Water TreatmentFluid MechanicsWater & WastewaterSewer credit for water a tower evaporates: the volume that never reaches the drain, valued at the municipal sewer rate.

Net Water and Sewer Cost of a Cooling Tower

C=Vm pw+(Vm−Ve) psC = V_m \, p_w + (V_m - V_e) \, p_s

Water TreatmentFluid MechanicsWater & WastewaterFull water and sewer bill for a cooling tower: makeup charged at the water rate, plus only the volume actually discharged at the sewer rate.

Total Water Treatment Program Cost

C=Cw+Cp+CeC = C_w + C_p + C_e

Water TreatmentChemistryFluid MechanicsTotal operating cost of a treated cooling system: the water and sewer bill, the chemical invoice and the energy bill added together.

Prandtl Number

Pr=μcpk\mathrm{Pr} = \frac{\mu c_p}{k}

Heat TransferFluid MechanicsThermodynamicsFluid property group comparing how fast momentum diffuses with how fast heat does, setting the relative thickness of the two boundary layers.

Nusselt Number

Nu=hLk\mathrm{Nu} = \frac{h L}{k}

Heat TransferFluid MechanicsThermodynamicsDimensionless convection coefficient: the ratio of convective transfer at a surface to pure conduction through the same fluid layer.

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.

Pore Water Pressure (u = γw zw)

u=γwzwu = \gamma_w z_w

Soil MechanicsFluid MechanicsHydrostatic pore water pressure at a point below a static water table, from the depth of water standing above it.

Submerged (Buoyant) Unit Weight

γ′=γsat−γw\gamma' = \gamma_{sat} - \gamma_w

Soil MechanicsFluid MechanicsEffective or buoyant unit weight of soil below the water table, the saturated unit weight less the uplift of the water it displaces.

Hydraulic Gradient

i=ΔhLi = \frac{\Delta h}{L}

Soil MechanicsFluid MechanicsHydraulic gradient as the loss of total head divided by the length of the flow path, the dimensionless driving force behind all seepage.

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.

Seepage Velocity from Discharge Velocity

vs=vnv_s = \frac{v}{n}

Soil MechanicsFluid MechanicsActual seepage velocity through the pores, obtained by dividing Darcy's fictitious discharge velocity by the porosity of the soil.

Equivalent Horizontal Permeability of Layered Soil

keq=k1H1+k2H2H1+H2k_{eq} = \frac{k_1 H_1 + k_2 H_2}{H_1 + H_2}

Soil MechanicsFluid MechanicsThickness-weighted equivalent permeability for flow parallel to the bedding of two soil layers, the parallel-resistance case of stratified seepage.

Time Factor for Consolidation

Tv=cv tHdr2T_v = \frac{c_v\,t}{H_{dr}^{2}}

Soil MechanicsFluid MechanicsDimensionless time factor of Terzaghi consolidation theory, with the coefficient of consolidation entered in m²/s and the longest drainage path.

Time Factor from Degree of Consolidation (U ≤ 60%)

Tv=π4(U100)2T_v = \frac{\pi}{4}\left(\frac{U}{100}\right)^{2}

Soil MechanicsFluid MechanicsTerzaghi's parabolic approximation relating the time factor to the average degree of consolidation, valid for U of 60 percent or less.

Hydraulic Detention Time

t=VQt = \frac{V}{Q}

Water & WastewaterWater TreatmentFluid MechanicsTheoretical detention time of a tank, clarifier or contact basin: the working volume divided by the flow passing through it.

Surface Overflow Rate

vo=QAv_o = \frac{Q}{A}

Water & WastewaterWater TreatmentFluid MechanicsSurface overflow (surface loading) rate of a settling basin — flow divided by plan area, reported here in metres per day.

Filtration Rate (Filter Loading Rate)

vf=QAv_f = \frac{Q}{A}

Water & WastewaterWater TreatmentFluid MechanicsFiltration rate through a granular media filter: flow divided by filter bed area, the approach velocity reported in metres per day.

Backwash Water Volume

Vbw=vb A tV_{bw} = v_b \, A \, t

Water & WastewaterWater TreatmentFluid MechanicsWater consumed by one filter backwash, from the backwash rise rate, the filter bed area and the duration of the wash.

Trickling Filter Hydraulic Loading

Lh=Q+QrAL_h = \frac{Q + Q_r}{A}

Water & WastewaterWater TreatmentFluid MechanicsHydraulic loading on a trickling filter including recirculation — total flow per unit of media surface area, in metres per day.

Per-Capita Wastewater Flow

q=QPq = \frac{Q}{P}

Water & WastewaterWater TreatmentFluid MechanicsAverage wastewater contributed per person per day, from the plant flow and the population served, reported in gallons per capita per day.

Harmon Peaking Factor

PF=1+144+P/1000PF = 1 + \frac{14}{4 + \sqrt{P/1000}}

Water & WastewaterWater TreatmentFluid MechanicsHarmon peaking factor for sanitary sewer design: the ratio of peak hourly to average daily flow for a served population.

Manning's Equation for Velocity

v=1nR2/3S1/2v = \frac{1}{n} R^{2/3} S^{1/2}

Water & WastewaterFluid MechanicsOpen-channel velocity by Manning's equation in SI form, from the roughness coefficient, hydraulic radius and channel slope.

Manning's Equation for Flow

Q=1nAR2/3S1/2Q = \frac{1}{n} A R^{2/3} S^{1/2}

Water & WastewaterFluid MechanicsOpen-channel discharge by Manning's equation in SI form, from flow area, roughness, hydraulic radius and slope.

Francis Formula: Rectangular Weir

Q=3.33 L H3/2Q = 3.33 \, L \, H^{3/2}

Water & WastewaterFluid MechanicsFlow over a suppressed rectangular weir by the Francis formula, with the trade constant 3.33 for crest length and head in feet.

V-Notch (Triangular) Weir Flow

Q=815Cd2g tan⁡ ⁣θ2 H5/2Q = \frac{8}{15} C_d \sqrt{2g} \, \tan\!\frac{\theta}{2} \, H^{5/2}

Water & WastewaterFluid MechanicsDischarge over a sharp-crested triangular weir from the notch angle, head and discharge coefficient, in the standard theoretical form.

Parshall Flume Free Flow

Q=4 W H1.522 W0.026Q = 4 \, W \, H^{1.522 \, W^{0.026}}

Water & WastewaterFluid MechanicsFree-flow discharge through a Parshall flume of 1 to 8 ft throat width, with W and the head H in feet and Q in cubic feet per second.

Stokes Settling Velocity

vs=g(ρs−ρ)d218μv_s = \frac{g (\rho_s - \rho) d^2}{18 \mu}

Water & WastewaterFluid MechanicsTerminal settling velocity of a small sphere in laminar flow by Stokes' law — the grit chamber and clarifier design relation.