Relationship between flow rate and pressure in fire service pumps I'm trying to get an explanation (at a suitable level please!) for something we have recently come accross. In general in the Fire Service we are taught that if you increase the presure of water coming out of our pumps you will also increase the flow rate ie ammount of water.
We recently discovered in the manurfactures guidance that our pump is capable of delivering a much higher flow rate at a lower pressure. 
Our pump can deliver 800 litres per minute at 5 bar pressure or 1400 litres per minute at 1 bar.
Can someone please explain the physics behind this and we would be very grateful.
Thanks
 A: This sounds like a centrifugal pump.  If so, this type of pump has a published pump curve, which tells what flow rate can be achieved relative to discharge pressure.  For an intro to pump curves, see https://blog.craneengineering.net/how-to-read-a-centrifugal-pump-curve.
Regarding the concepts involved (no equations), it is a known fact that the pressure drop in a pipe is proportional to the flow rate squared (assume turbulent flow).  This means that if you double the flow rate in a pipe of given length, diameter, etc., you will find that the pressure drop through the pipe increases by a factor of 4.  The same will also apply for the pump, which will have its own pressure drop.
For low flow rates, the nozzle on the end of the water line will be constricted, so most of the pressure drop will be taken at the nozzle, and all pressures before the nozzle will be relatively high.  For higher flow rates, the piping and pump will experience more pressure drop, and the pressure at the nozzle will be lower as a result.
The highest achievable pressure to be obtained from a centrifugal pump occurs when the flow rate is zero, which is known as "dead head" pressure.  This maximum pressure depends on the pump's impeller diameter and rpm.  For an electrically driven centrifugal pump that does not have a variable speed driver connected to it, the rpm is fixed, so increases or decreases in dead-head pressure are achieved by changing the impeller diameter.
Obviously, nobody would run the pump at its dead-head pressure because no flow rate occurs under these conditions.  The pump is expected to deliver a desired flow rate at a specified nozzle pressure.  If you find that the pressure is too low at the desired flow rate, this can be fixed by buying and installing a larger diameter pump impeller, if you are not already at the maximum impeller size that the pump case can handle.
A: Agree with David White's reply, here is some additional background which may be helpful. 
The job of the pump is to turn shaft horsepower into water movement. Horsepower at the pump shaft is the product of a flow (RPM) and an effort (torque) variable. Horsepower at the water outlet is the product of a flow (pounds per hour) and an effort (pounds per square inch) variable. 
How do these vary with the speed with which the pump is running? Let's look at the limiting cases: no hose connected to the pump, and hose outlet blocked. 
The no hose case represents the condition where the pump output is not connected to a load of any kind- the water runs free. In this case the pump is producing no useful work except that required to pull water through it: lots of flow, almost zero pressure. 
The blocked outlet case represents the condition where the flow from the pump is not allowed to drive a load of any kind- the water goes nowhere. In this case the pump is producing no useful work except that required to pressurize the blocked outlet pipe: No flow, lots of pressure. 
At both of these extremes, then, the delivered power of the pump is zero.
Remembering that power = effort times flow,  we then ask when is this product a maximum? To maximize the product of two numbers requires that we simultaneously maximize the magnitude of both numbers, which means that the best match of the power in to the power out occurs when the pressure and the flow rate both go through their maxima which occurs somewhere between the two minima that bound the power curve. This is the "design point" of the pump. 
If we then reduce the load by opening up the nozzle, we get more flow- but at lower pressure. If we increase the load by closing down the nozzle, we get less flow- but at higher pressure. 
From here, the analysis can be expanded by going into the details of how the pump works and how the driving engine's power output varies with speed and load, but the general principles outlined above hold regardless of the engine's and the pump's interior workings.  
