This is simplified and doesn't account for the differences in the flow rates of different sizes of hydraulic cylinders at a given pressure but should adequately demonstrate how hydraulic forces work in syringes. I've arbitrarily chosen whole numbers for the sake of clarity. I don't think anyone will be injecting with a syringe that's plunger has an area of 6 in^2. Well, Manwhore might use one for tren but he'd be the only one.
To determine the force of a cylinder, use this formula: F = p x A
F = force in pounds (how hard you have to push on the plunger)
p = pressure in psi (pressure in the syringe chamber. I'll use 3 psi to keep it simple)
A = area of cylinder piston (I'll use 3 in^2 for the small cylinder and 6 in^2 for the large one)
For the smaller cylinder:
F = p x A
F = 3psi x 3 in^2
F = 9 lbs
It takes 9lbs of force applied to the plunger of the small cylinder to produce a pressure of 3 psi on the cylinder chamber.
For the larger cylinder:
F = p x A
F = 3psi x 6 in^2
F = 18 lbs
It takes 18lbs of force applied to the plunger on the large cylinder to produce a pressure of 3psi on the syringe chamber.
So it takes twice as much force applied to the large cylinder to produce the same pressure as the small cylinder. If you increase the force applied to the small cylinder to 18lbs, you'll double the pressure to 6 psi on the cylinder chamber and the flow rate will equal that of the larger cylinder.
Apologies for any errors. It's Friday night and ETOH is in the mix.