Will flow rate always increase if the pressure drop across piping system is decreased? I have a test stand that is used for testing hydraulic pumps. We are adding a pump that we have never tested before and we are getting low flow readings. Will increasing piping to one size bigger than the pump outlet on our test stand increase the flow? My thought is it would reduce the pressure drop across the test stand piping system allowing a higher flow rate. 
 A: In a straight pipe, the Darcy-Weisbach equation gives you less pressure drop for larger diameter, but if you want to increase flowrate by enlarging pipe while keeping power consumption constant, you have to understand where most of the pressure drop happens, and that depends on specifics. The connection between large and small diameter pipes has a lot of pressure drop, but if your pipe is very long this might not be significant. So you have to do the math because there is no straight answer.
A: You need to pay attention to the whole path of the fluid. Even increasing the pipe diameter it does not necessarily means the flow will increase at the same rate. If you have a nozzle or some other geometric difference in the way, this element will be responsible for the major part of the drop. 
Regardless of how you are improving the losses on the pipe part, that nozzle or that element will always prevent the whole fluid from being faster.
Also it's worth to notice that every change in the diameter will cause a pressure drop, even if it goes from a small diameter to a bigger one. So making the pipe larger could not be so effective at some point (because the pump outlet has a smaller diameter).
A: Before considering increasing pipe size, determine what kind of pump you have.  If you have a positive displacement pump (which is probable for a hydraulic pumping application), you will find that the discharge pressure will vary to ensure that a constant flow rate is maintained.  This means that the limiting factor is how fast the mechanical parts (probably a piston) can send flow out of the pump, and increasing discharge piping diameter will have very little effect.
There is one other thing to check.  For a positive displacement pump, there is probably a relief valve to prevent over-pressuring the discharge side of the pump.  The relief valve will most likely be routed from the pump discharge, back to the pump suction.  If the relief valve is leaking or the relief setting is set too low, the resulting recycle flow will reduce the forward flow that you should be getting.
