We will install a filter in the pipeline through which water flows. This filter acts as an obstacle to the flow of water. There will be pressure gauges before and after the filter, and we want to understand the relationship between the differential pressure (in kgf/cm^2) and the flow rate (Q)(in L/min) measured by the flow meter installed before the filter.

Now, here are the questions:

• If we increase the pressure of the pump that delivers water, we expect the flow rate (Q) passing through the filter to increase, and the corresponding differential pressure (P) to also increase. In this case, does the relationship follow Bernoulli's theorem, given by Q = kP? Here, k represents a device-specific constant. Or, can we consider the filter as simply a resistance element, where the flow rate and differential pressure are directly proportional?
• If we keep the pump pressure constant and push out the water, would the flow rate (Q) gradually decrease due to frictional resistance inside the pipes? If the flow rate (Q) decreases, would the constant value of k in the equation Q = kP remain the same in this case?
• Are there any situations where increasing the pump pressure no longer increases the flow rate through the filter?