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

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To calculate the force in a hydraulic system, the relationship between the areas of the pistons and the forces acting on them is crucial. The formula used is F1 = (A1/A2) * F2, where A1 and A2 are the areas of pistons 1 and 2, respectively. In this case, with piston diameters of 0.34 in and 1.0 in, the correct calculation yields a force of 57.8 pounds to support a 500 lb weight over piston 2. It's important to ensure that units are consistent, particularly if converting to Newtons, which requires changing inches to meters. This approach confirms the validity of the calculations in hydraulic systems.
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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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