Pressure upstream and downstream of a filter

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Aptx4869
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Dears I have one question

When a filter gets clogged, the upstream pressure will go up. But what happens to the downstream pressure ? does it go down or stays the same in case of positive displacement pump vs centrifugal pumpThanks
 
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Sorry I forgot to mention that information. The filter is on the discharge side. Let's take this system as an example. I put marks on the pump and the filter

thanks
 

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Any idea please ?

Assuming the filter is on the discharge side and the only change in the system is that the filter is getting dirty. What happens to downstream pressure in case of

1) There is pressure regulator upstream the filter.
2) There is no pressure regulator, centrifugal pump vs positive displacement
 
In a nutshell the rest of the answer can be predicted by the use of the system and the flow rates. A clogged filter will act very similar to an orifice plate. A good system design will have some allowance for clogging and still maintaining system serviceability. This "overdesign" combined with the expected use conditions is a part of the service interval as prescribed by the designer.
If the device that is downstream of the filter uses less fluid than resultant orifice's remaining at the pressure delivered you will see very little change. This is due to the pump still being able to continue delivering the required flow. If the device requires more fluid than is able to pass the orifice the pressure will drop downstream until the system returns to a balanced state. Many designers use a an upstream pressure gauge and a downstream one to show drop across the cartridge. A small amount is expected however as plugging continues it is larger and more highly dependent on flows.
Also, looking at your diagram quickly it should be considered that either multiple devices or operator habits can affect this. Several devices can sum to a greater flow requirement than can pass the plugging. This would be observed when all operates as expected individually or in small combinations and then more functions slows everything. Prior history is key here as this same condition may be from insufficient pump output.
The operation also can be a factor if human controlled. One person may be very gentle in operation application and especially at multiple functions and the low flow rate allows quite clogged filters to function. Another may use several full flow commands and see pressure drops with minimal filter blockage.

Hopefully you are starting to see the orifice like conditions that a plugged filter emulates.
 
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In general as a filter clogs the pressure drop across it increases. If the pump has excess pressure potential, and specifically is controlled by the downstream pressure, then it can remain the same up to a point. It really depends on the rest of the system though.

In your post though you state the regulator is upstream. So the pressure downstream will drop, as will the maximum flow rate.