We can build the model in a spreadsheet simulating ten layers in the filter. For each layer we calculate the headloss with Carmen-Kozeny and calculate from this the pressures as a function of the place in the filter. Calculate the headloss and the actual pressure in each layer for a clean bed of the filter bed. Assume the following:

water height above filterbed: 1 m
height of the filterbed: 1 m
height of a layer in the filterbed: 0.1 m
superficial velocity: 10 m/h
grain size: 1 mm

To calculate the headloss and actual pressure in each layer of the filter bed for a clean bed, we can follow these steps:

Step 1: Calculate the velocity of water passing through each layer:
- Convert the superficial velocity from meters per hour to meters per second:
Superficial velocity = 10 m/h = 10 / (60 × 60) m/s = 0.00278 m/s

Step 2: Calculate the porosity (void fraction) of the filter bed:
- The porosity can be estimated using the grain size:
Given grain size = 1 mm = 0.001 m
Porosity = 1 - (grain size / height of a layer)
= 1 - (0.001 / 0.1)
= 1 - 0.01
= 0.99 (or 99%)

Step 3: Calculate the hydraulic radius of each layer:
- The hydraulic radius is a measure of the flow area available for water to pass through in a given layer.
Hydraulic radius = (height of a layer × porosity) / (2 × pore spacing)

In this case, we assume the filter bed consists of uniform grain size, so the pore spacing is equal to the grain size.

Hydraulic radius = (0.1 × 0.99) / (2 × 0.001)
= 0.099 / 0.002
= 49.5 m

Step 4: Calculate the velocity headloss across each layer using the Carman-Kozeny equation:
- The Carman-Kozeny equation relates the headloss in a porous filter bed to the velocity and hydraulic radius.

Headloss = (K × velocity^2) / (hydraulic radius^2)

K is a constant that depends on the shape and packing of the particles in the filter bed. For simplicity, let's assume a value of 0.3.

Headloss = (0.3 × (0.00278)^2) / (49.5^2)
= 0.000000077 m (or 0.077 Pa)

Step 5: Calculate the pressure at the bottom of each layer:
- The pressure at the bottom of each layer is equal to the pressure at the top of the previous layer minus the headloss across that layer.

Pressure at bottom = Pressure at top - Headloss

We start with a water height above the filter bed of 1 m, so the pressure at the top of the first layer is the pressure due to the height of water column above it.

Pressure at top of first layer = water density × gravity × water height above filter bed
= 1000 kg/m^3 × 9.8 m/s^2 × 1 m
= 9800 Pa (or 9.8 kPa)

Pressure at bottom of first layer = 9800 Pa - 0.000000077 m = 9.8 kPa

The pressure at the bottom of the second layer would be equal to the pressure at the top of the first layer minus the headloss across the first layer, and so on...

Continue this process for each layer (up to the tenth layer) by subtracting the headloss of the previous layer from the pressure at the top of that layer. Each layer's pressure is obtained by calculating the headloss using the Carman-Kozeny equation, and then subtracting it from the pressure at the top of the layer above.