The historical domestic filter illustrated by Hiscox uses a barrel containing sand and charcoal above a supported screen. Water descends through the layers and enters a lower collection space. The cutaway shows water passing through the gravity-fed bed and draining into the space below.
Domestic Filter Interactive Calculator
Explore a historical layered gravity filter in cutaway. Enter an equivalent bed diameter, media depth, maintained water depth and measured conductivity of the complete bed. The calculator applies a saturated, constant-area Darcy model; it does not estimate contaminant removal.
Equation Used
- Steady saturated flow, with Darcy behavior and negligible side leakage.
- Equivalent constant circular flow area, despite the illustrative barrel outline.
- Water level above media is maintained by an external supply.
- Atmospheric pressure at the free-draining bed outlet; no downstream backpressure.
- Equivalent conductivity includes the complete media bed and fluid, but excludes additional screen and outlet resistance.
- Flow markers are explanatory and do not represent particle residence time.
Historical construction is shown for explanation. Flow results do not establish water quality, contaminant removal or drinking-water suitability. The conductivity must describe the complete bed and actual fluid; it is not supplied by the drawing.
Layers, support and collection space
The cutaway identifies an upper sand layer, a middle charcoal layer and a lower sand layer. A mesh and supporting frame retain the media above the collection space. A side outlet receives the drainage below the screen.
The water level above the media remains at the selected height in this steady-flow model. Animated markers indicate downward movement through the bed and drainage to the outlet. They are not individual particles and do not show removal of any substance.
The barrel shape and screen details follow the historical arrangement. For calculation, the bed is simplified to a cylinder with the entered equivalent diameter and total depth. Its displayed dimensions are annotated; the drawing is not a fabrication specification.
Comparing porous-bed flow
The calculator compares how equivalent area, water head and measured hydraulic conductivity affect the ideal flow through a saturated bed. It is a hydraulic example for a historical device.
Conductivity must be measured or established for the actual complete bed and fluid. Sand and charcoal names alone do not determine it. The page does not assign contaminant-removal efficiency, service life or drinking-water approval.
Include elevation in the driving head
Take the bottom of the saturated bed as the zero-elevation reference. Its free-draining outlet is at atmospheric pressure. The water free surface is L+h above it, so the total head difference is L+h, not just the ponded depth h.
The hydraulic gradient is J=(L+h)/L. Darcy superficial flux is v=KJ, and flow is Q=Av with A=πD²/4. The numerical conversion from mm³/s to L/min is 60/1,000,000.
Superficial flux uses the entire bed area. It is not the actual speed through individual pores. The model treats the layered bed as a single equivalent resistance and assumes no added restriction at the screen or outlet.
At zero pond depth, J=1 and v=K under the stated saturated, maintained-supply assumptions. An unwatered bed that drains and becomes unsaturated is a different problem.
A numerical comparison
For an equivalent 300 mm diameter, the area is approximately 706.9 cm². With a 200 mm bed and 150 mm maintained pond depth, J=(200+150)/200=1.75.
If measured conductivity is 0.1 mm/s, superficial flux is 0.175 mm/s and ideal flow is approximately 0.742 L/min. Doubling conductivity doubles that result. Doubling diameter multiplies it by four.
Changing conductivity to zero stops the illustrated flow. The area and head gradient remain defined because the geometry and water levels have not changed.
Where the model stops
Real layered beds can compact, clog, leak at the walls or become partly unsaturated. Screen resistance, an outlet restriction and a rising collection-water level can change the available head. The single equivalent-conductivity model does not solve those effects.
The historical layer arrangement is not presented as a modern treatment recommendation. A hydraulic flow estimate cannot establish the quality of the outlet water. The animated markers show flow direction only; they do not indicate contaminant removal.
Domestic filter questions
What type of filter is illustrated?
The illustration shows a gravity-fed barrel with sand and charcoal layers over a supported screen and collection space.
What is equivalent diameter?
It specifies the constant circular flow area used by the simplified calculation, rather than the varying width of the drawn barrel.
What does conductivity mean?
It is the proportionality between superficial flux and hydraulic gradient for the bed and fluid under the stated flow conditions.
Why does zero pond depth still give flow?
The bed’s elevation drop still gives unit gradient when it remains saturated and continuously supplied.
Does this calculate water treatment performance?
No. It calculates an idealized flow rate only.
References
Hiscox, Mechanical Movements, Powers, Devices and Appliances, mechanism 580, printed page 156 (PDF page 166): layered domestic barrel filter.
USGS, Introduction to Ground-Water Hydraulics, Part II: Darcy’s Law: specific discharge, hydraulic gradient and conductivity. The constant-area bed and boundary conditions are explicit assumptions of this calculator.
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