OK Frantz, Lets see if I can apply the basic principles as you have described them.
Take a guy that weighs 200 lbs whose feet are 10 inches long and 5 inches wide (this is just an example not a custom boot order). With both feet flat on the ground that is 200 lbs "distributed" over 100 sq inches. Following your example that becomes 100 X 200 or 2000 lbs. When this guy stands on something it compresses the something until equilibrium is reached. Lets say he stands on a bathroom scale. Why doesn't the scale register 2000 lbs? Or better yet, since, by your approach, the scale would have to push up at 2000 lbs and he only weighs 200 lbs, why doesn't he get thrown upward with an initial acceleration of something like 10 G's???
I by no means wish to "talk down to you", but my first co-major was physics and math and while your arithmetic remains flawless your analysis is bassakwards. There is just a simple misunderstanding here. It happens to me a lot but this time it didn't.
Now then, if we had a hydraulic cylinder in a static situation (not currently extending or retracting so there are no dynamic losses) then the force on the piston (ram) would be equal to the pressure in the fluid times the area of the piston. A larger piston would "multiply" the force proportionately more, increasing as the square of the diameter. This is sort of a fair "fit" to your contention but this hydraulic cylinder example does NOT model the situation we are discussing.
The cider press doesn't care how the force is applied, by hydraulic cylinder, screw jack, or an inverted pyramid of Lithuanian acrobats with SCUBA weights on their waists. The force applied to the "sqeezing chamber" can come from anywhere, it is an issue of convenience (and my laziness) that I consider a hydraulic ram or air/hydraulic jack.
Whatever linear force is applied to the "crushing piston" is distributed (divided up equally) over the surface of the piston and then since the fruit acts essentially like a liquid (untill nearly finished pressing) the pressure in the fruit (in psi) is the same as on the face of the piston which is the area of the piston divided into the psi.
AHA, a small light came on in what's left of my brain. Something that always helped me learn and teach about solving physics and engineering problems involving lots of units was to include the units in the calculations. For example, if you divide pounds by square inches you get psi. If you expected psi as the answer then you might have worked the problem correctly. If you made a booboo and reversed the numerator and denominator or multiplied instead of divided your answer would be in units of either: square inches per pound or square inch pounds and you would know their was an oops. Getting the units right isn't proof that the numbers are right but not getting the right units is proof that the calculation was set up incorrectly. (There is still a small problem with me and units. I have a lot of left over square radians from years of physics homework and tests. I never needed these for anything and they are apparently useless surplus.)
Put the units in with your good math and see if you accept the results of how the units turn out.
Meanwhile, I still haven't found out a practical pressure for sqeezing pears but am hoping to do so soon.
Patrick
Take a guy that weighs 200 lbs whose feet are 10 inches long and 5 inches wide (this is just an example not a custom boot order). With both feet flat on the ground that is 200 lbs "distributed" over 100 sq inches. Following your example that becomes 100 X 200 or 2000 lbs. When this guy stands on something it compresses the something until equilibrium is reached. Lets say he stands on a bathroom scale. Why doesn't the scale register 2000 lbs? Or better yet, since, by your approach, the scale would have to push up at 2000 lbs and he only weighs 200 lbs, why doesn't he get thrown upward with an initial acceleration of something like 10 G's???
I by no means wish to "talk down to you", but my first co-major was physics and math and while your arithmetic remains flawless your analysis is bassakwards. There is just a simple misunderstanding here. It happens to me a lot but this time it didn't.
Now then, if we had a hydraulic cylinder in a static situation (not currently extending or retracting so there are no dynamic losses) then the force on the piston (ram) would be equal to the pressure in the fluid times the area of the piston. A larger piston would "multiply" the force proportionately more, increasing as the square of the diameter. This is sort of a fair "fit" to your contention but this hydraulic cylinder example does NOT model the situation we are discussing.
The cider press doesn't care how the force is applied, by hydraulic cylinder, screw jack, or an inverted pyramid of Lithuanian acrobats with SCUBA weights on their waists. The force applied to the "sqeezing chamber" can come from anywhere, it is an issue of convenience (and my laziness) that I consider a hydraulic ram or air/hydraulic jack.
Whatever linear force is applied to the "crushing piston" is distributed (divided up equally) over the surface of the piston and then since the fruit acts essentially like a liquid (untill nearly finished pressing) the pressure in the fruit (in psi) is the same as on the face of the piston which is the area of the piston divided into the psi.
AHA, a small light came on in what's left of my brain. Something that always helped me learn and teach about solving physics and engineering problems involving lots of units was to include the units in the calculations. For example, if you divide pounds by square inches you get psi. If you expected psi as the answer then you might have worked the problem correctly. If you made a booboo and reversed the numerator and denominator or multiplied instead of divided your answer would be in units of either: square inches per pound or square inch pounds and you would know their was an oops. Getting the units right isn't proof that the numbers are right but not getting the right units is proof that the calculation was set up incorrectly. (There is still a small problem with me and units. I have a lot of left over square radians from years of physics homework and tests. I never needed these for anything and they are apparently useless surplus.)
Put the units in with your good math and see if you accept the results of how the units turn out.
Meanwhile, I still haven't found out a practical pressure for sqeezing pears but am hoping to do so soon.
Patrick