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