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			The pressure in the line between the injection pump and the injector will rise 
yes the pressure will rise, but the pressure is predetermend by the injector crack pressure. Pump pressure or injection pressure will not change it self just because you have more pressure in the cylinder.
BTW, nozzles convert pressure in the fluid to velocity, and the energy is converted to kinetic energy. So the pressure drops across the nozzle from high pressure to the pressure inside the combustion chamber while the fuel is injected.
			
		
	
 I think this statement is not quite correct, as the fuel is pressurized from the plunger in the fuel pump it lifts the delivery valve of it's seat and fuel is passed through the injector line, when the pressurized fuel lifts the injector needle of it's seat the fuel passes through the holes in the nozzel its converted to a mist, there is no drop in pressure until the helix on the plunger passes the spill port, this causes a rapid drop in pressure and the delivery valve in the pump closes this stops the flow to the injector and the needle closes ceasing injection, once injection finishes you would have the nozzle under the same pressures as the combustion chamber but only when injection has finished.