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Mechanical operations and solids · McCabe–Smith–Harriott

Particle sizing and distribution models

particle size distribution calculator

D32 · Sauter

—

mm

D43

—

mm

D10

—

D50

—

D90

—

Rosin–Rammler

n = — · De = — mm · R² = —

Gates–Gaudin–Schuhmann

m = — · Dmax = — mm · R² = —

Pasante acumulado semilog

Differential retained distribution

Particle size breakdown

#Dp (mm)D̄p (mm)mi (g)xiPasante Yi

Coe–Clevenger · Kynch · Richardson–Zaki

batch sedimentation calculator

Required area

—

m²

Critical Z

—

m

critical t

—

min

tu

—

min

vt Stokes

—

m/s

v impedida

—

m/s

Target height Zu = — m · Re terminal = — · n recomendado = —

Derivation and area by concentration

#t (min)Z (m)v (m/h)C (kg/m³)A (m²)

Constant pressure and compressible cake

filtration equation calculator cake resistance

Kp

—

s/m⁶

B

—

s/m³

R²

—

α torta

—

m/kg

Rm

—

m⁻¹

Index s

—

R² comp. —

Regression by pressure level

ΔP (kPa)Kp (s/m⁶)B (s/m³)R²α (m/kg)Rm (m⁻¹)
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Particle size analysis

Sauter mean diameter calculator

D32 preserves the surface-to-volume ratio of the population and is particularly relevant in mass transfer, combustion and particle entrainment.

Espesamiento

Coe-Clevenger thickener design calculator

The controlling area is the maximum computed across the physically valid concentration range of the test.

Filtration

Compressible cake model

Several pressure levels allow the index s to be estimated by logarithmic regression of α against ΔP.

Preguntas frecuentes

Mechanical operations FAQ

What does the Sauter diameter D32 represent?⌄

It is the diameter of a sphere with the same volume-to-surface ratio as the whole distribution. With mass fractions and uniform density: D32 = 1/Σ(xi/D̄pi).

How does Richardson–Zaki work?⌄

Corrects the isolated terminal velocity for a suspension: v = vt εⁿ. The voidage ε lowers the velocity and the exponent n depends on the terminal Reynolds number.

What does cake compressibility mean?⌄

A compressible cake increases its specific resistance with pressure: α = α0(ΔP)ˢ. s≈0 indicates an incompressible cake; larger values indicate greater sensitivity to pressure.