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razan1016
#1 Posted : Friday, June 10, 2016 4:11:53 AM
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Hey,

SO i was reviewing the concept behind pascal's principle and hydraulic lift. I understand that due to pascal's principle we will have constant uniform pressure in all pistons. And that, when pressure is held constant, Force and Area are inversely proportional. With that in mind, how is it that when Piston 2 has a greater area than piston 1 is also has greater force output?

thanks,
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jaredenns
#2 Posted : Friday, June 10, 2016 6:24:53 PM
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razan1016 wrote:

...when pressure is held constant, Force and Area are inversely proportional.


I think your confusion has arisen in this sentence. The formula for pressure as it applies in this case is:

P = F/A

So, if we hold pressure constant, than we see that force is proportional to area. In other words, if I increase force, area has to increase as well in order to maintain the equality (I've increased the top of my fraction so I am forced to divide by a larger number to balance it out).

Just because force and area are related by a fraction, does not necessarily mean that they are inversely proportional: it can look that way at a glance, but it is important to keep track of what is being held constant and what has to change as a result.

Cheers,
Jared
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mahdismaleki
#3 Posted : Saturday, June 11, 2016 3:31:03 PM
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Hi there,

If you write out the formula that we had: F(in).r(in) = F(out).r(out) , in this case it's not the surface area (A) which is our r (or the distance over which force is applied); our distance (r) is how far down we push the (in) piston and how far the (out) piston moves upwards. This distance is inversely proportional to surface area, since the same volume of fluid is moving from one piston to the other (Volume= surface area x height) and to clarify, height is the same as "r" here, the distance over which we apply the force, we are pushing the piston vertically.

Hope this helps!
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