I am in need of assistance for a project dealing with a sandbed filtration system.
First off there are three parts to the project, the first being to show pressure drop across the filter as a function of void fraction, the second showing void fraction as a function of water filtered and the third being several steps. No issues with the first and second part, but the third step is a system that does not have a constant flow rate or constant pressure drop across the filter, a scenario we have not encountered yet.
We are given the dimensions for the filter, which is horizontal, an initial flow rate of 30GPM, and a pump curve, initial void fraction (0.38) , and concentration of suspended solids (0.12%). We are asked to determine the time required before backwashing is necessary once a certain pressure drop (47psi) is reached across the bed, the flow rate at that time, the amount of waste water filtered to that time, and the weight of solids removed.
We have equations to solve for the system if either flow rate or pressure drop is constant, but I need help since the system is varying flow rate and pressure drop across the filter.
Any guidance would be greatly appreciated.
Thanks.