If you take the same setup and apply the 10 psi to a 0.5 square inch
piston you are now getting 10 lbs per 1/2 square inch which is 20 psi and
you get 20 lbs. of force out of the system.
No, you don't. This is nonsense. If you have a pressure of 10 psi (that's
pounds per square inch), you have a pressure of 10 pounds per square inch,
over every single bit of area in the entire system. The insides of the brake
or clutch line, the bore of the fittings, against the base of the bleed screw,
*any* area inside the system will have that same force.
If that pressure is applied to 1 square inch, you get 10 pounds of force.
If that pressure is applied to 2 square inches, you get 20 pounds of force.
If that pressure is applied to 1/2 square inch, you get 5 pounds of force.
The force in pounds is the product of the area times the pressure, simple,
basic high school math. Write out the equation, and see how the units cancel:
pounds pounds inch * inch
Force ------- = Pressure ----------- x Area ------------
1 inch * inch 1
This is classic Newtonian physics. The work that goes in is the same as
the work that comes out. That is, negating the effects of mechanical friction
and things like the force used to distort the clevis, the pins, etc. on every
pedal application. Here I use work in the classic physics definition, a force
applied over a distance.
People are confusing volume, pressure, area and distance in the situation.
They are all related by basic mathematical equations.
mjb.
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