Joe
Perhaps the confusion here is because we seem to be mixing apples,
oranges, pear, peaches, and potatoes (needed a vegetable).
In these situation there are really three different balances that take
place, not just an energy balance. These is a mass balance (amount of fluid).
You have an energy balance related to the amount of forces being applied. The
third equation deals with a momenteum balance (dealing with mass and
acceleration). In full mathematical form the equations take both sides of an
engineering textbook.
The balancing of forces in this situation is really between your foot's
force on the pedal and the resistive forces on the racecars brake or clutch
plus the resistive forces (frictional losses due to bends, diamter changes,
etc) in the hydraulic lines. In both brake/clutch cases, we are dealing with
applied and resistive forces that involve leverage. From my perspective, the
pedal force is being applied through the slave cylinder's rod (a much smaller
diameter) which engages the clutch.
In a closed system, changes in diameter do impact the travel distance. So
the fluid in a large master cylinder will occupy proportionately more space
in a smaller feed line and smaller slave cylinder. The smaller the slave
cylinder, the more fluid movement would be greater than on a large slave
cylinder for the same amount of pressure. Resultantly, the slave cylinder's
size impacts the travel distance of the slave clinders rod for the same
amount of fluid movement out of the master cylinder (the mass balance).
The momenteum balance deals with the racecars movement. These equations
address the differences between such factors as braking at 80 mph and 180
mph. ot the difference between braking a car that weights 2000 lbs verses
3000 lbs.
My primary point here is that this is not just a situation of balancing
energy (forces/pressures) between master and slave cylinders. It is much more
complex than that from a full engineering perspective. Since it is over 30
years since I studied mass, energy, and momenteum balances and never had a
mathematical application for the last 25, I can not go into this in more
detail. Perhaps there is another FOT member who can explain this better.
Best wishes, Cary
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