What is the Formula for Calculating Force in a Hydraulic System?

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SUMMARY

The formula for calculating force in a hydraulic system is derived from the relationship between the areas of the pistons and the forces applied. Specifically, the correct formula is F1 = (A1/A2) * F2, where A1 and A2 are the areas of piston 1 and piston 2, respectively. In this discussion, the diameters of the pistons are 0.34 inches for piston 1 and 1.0 inches for piston 2. The calculated force necessary to support a 500 lb weight over piston 2 is 57.8 pounds, confirming the validity of the formula when applied correctly.

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starfish794
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Piston 1 has a diameter of 0.34 in. Piston 2 has a diameter of 1.0 in. In the absence of friction, determine the force, necessary to support the 500 lb weight over piston 2.

I used F(1) = pi(r1^2)/pi(r2^2)*F(2)

and got the wrong answer. I used radii of .17in and .5in. Is that the right formula? Do I need to convert the units to something else?
 
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Well if your force is in Newtons, then you would need to convert the inches to meters.
 
I get the same answer?

We know that F1=P A1 and F2=P A2, solve 2 for P, P = F2/A2 and substitute.

F1 = F2/A2 A1

I get 57.8 Pounds which makes sense.
 

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