Filtration Rate Calculator

Calculate filtration time, average flow rate, and cake thickness for constant-pressure filtration operations.

About this calculator

This calculator models constant-pressure cake filtration, where a slurry is pushed through a filter medium and solids build up as a resistive cake while the liquid — the filtrate — passes through. Filtration time comes from two resistances in series: a cake term that grows with the square of slurry volume (because a thicker, more resistive cake accumulates as more slurry passes through) and a filter-medium term that grows linearly with volume, both scaled by filtrate viscosity and reduced by pressure drop and filter area. The cake term dominates for high specific cake resistance or larger batch volumes, while the medium term matters most early in a filtration run or with very fine, low-resistance media.

Average Flow Rate is simply total volume divided by total time — a useful summary number, though it hides that real filtration slows continuously as cake builds, starting fast and tapering off rather than running at a constant rate. Cake thickness and filtrate volume both use a simplified fixed 5% solids fraction assumption rather than your slurry's actual concentration, so for slurries with meaningfully more or less solids content than that, treat both figures as rough estimates rather than precise predictions — the filtration time and flow rate, which don't depend on that assumption, are the more reliable outputs here.

Inputs

Slurry Volume to Filter

cu yd

Filter Area

sq ft

Specific Cake Resistance (α·c)

1/m²

Filter Medium Resistance

1/m

Pressure Drop

Filtrate Viscosity

Pa·s

Tab to move between fields

Results

Filtration Time

13 s

Filtrate Volume

0.95 m³

≈ 6 bathtubs

Average Flow Rate0.08 m³/s

Estimated Cake Thickness0.03 m

How to Use This Calculator

Enter the Slurry Volume to filter in m³ and the Filter Area in m².
Enter the Specific Cake Resistance (α·c) in 1/m² — obtain from filtration lab tests or literature. Typical values range from 10⁸ to 10¹² 1/m² depending on particle size and slurry concentration.
Enter the Filter Medium Resistance in 1/m — typically 10⁶ to 10¹⁰ 1/m for filter cloths and membranes.
Enter the Applied Pressure Drop in Pa across the filter.
Enter the Filtrate Viscosity in Pa·s — water at 20°C = 0.001 Pa·s.
Read the Filtration Time in seconds, Average Flow Rate in m³/s, and Cake Thickness in m to plan filter cycle time and equipment sizing.

How the result changes with Filter Area

Filter Area	Filtration Time	Filtrate Volume
1	51 s	0.95 m³
1.5	22.89 s	0.95 m³
3	5.89 s	0.95 m³
5	2.2 s	0.95 m³

What each input means

Slurry Volume to Filter: Total volume of slurry to be filtered.
Filter Area: Total effective area of the filter medium.
Specific Cake Resistance (α·c): Combined specific cake resistance and solids concentration term. Typical values: 10⁸ to 10¹² 1/m².
Filter Medium Resistance: Resistance of the clean filter medium to flow. Typical values: 10⁶ to 10¹⁰ 1/m.
Pressure Drop: Applied pressure difference across the filter.
Filtrate Viscosity: Dynamic viscosity of the filtrate liquid. Water at 20°C is 0.001 Pa·s.

How this is calculated

Worked example, using the default values

Identify Input Parameters
4 parameters
Slurry Volume to Filter = 1, Filter Area = 2, Specific Cake Resistance (α·c) = 10000000000, Filter Medium Resistance = 100000000 = 6 input(s) provided
Calculate Filtration Time
Filtration Time
13 = 13
Calculate Filtrate Volume
Filtrate Volume
0.95 = 0.95
Calculate Average Flow Rate
Average Flow Rate
0.0769 = 0.0769
Calculate Estimated Cake Thickness
Estimated Cake Thickness
0.025 = 0.025

Engine last updated August 30, 2026. Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does filtration time grow faster than volume as I filter more slurry?

The cake resistance term in the filtration equation scales with the square of slurry volume, because a thicker cake — which builds up in proportion to how much has already been filtered — adds its own resistance on top of what's already there. This is why real filtration runs start fast and progressively slow down, unlike a simple constant-rate process.

How much does the filter medium resistance actually matter compared to the cake?

It depends on their relative magnitudes and how far along the filtration run you are — the medium resistance term grows only linearly with volume while the cake term grows with volume squared, so the medium's contribution to total filtration time is proportionally larger early in a run and gets progressively swamped by cake buildup as filtration continues.

Is the estimated cake thickness reliable for sizing equipment?

It's a simplified approximation that assumes a fixed 5% solids fraction in the slurry regardless of your actual concentration, so it will understate cake thickness for a more concentrated slurry and overstate it for a more dilute one. Use it as a rough sanity check rather than a precise design figure, and verify against your slurry's actual solids content for real equipment sizing.

Why does raising the pressure drop reduce filtration time?

Pressure drop is the driving force pushing liquid through both the cake and the filter medium, so increasing it directly speeds up flow through both resistances — filtration time falls as pressure drop rises across its entire range, though real filter presses have practical pressure limits set by equipment strength and cake compressibility that this simplified model doesn't account for.

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