How can I determine the pressure in a hydraulic system?

Question

I am trying to do my physics homework and there's a problem that asks to find the pressure inside the fluid of the hydraulic system. I am given a single mass and a single piston diameter. My only problem is that I do not know which equation to use! I have two conflicting equations (One printing in a booklet I have and the other one given by my professor in class). The one given in class is Pressure = Force / Area
and:
Pressure In = Pressure Out
so
Force1 / Area1 = Force2 / Area2

However, the booklet I have says:
Pressure1 = Pressure 2
so
Force1 * Area1 = Force2 * Area2

(Earlier in this printout it does say that pressure = force/area but that is only the pressure exerted by the fluid it states where the other is for an enclosed liquid system)

I get two drastically different answers depending on which equation I use and I do not know which one is correct! If someone could please help me that would be great!

Also just to clairify, I am only given a single piston diameter which leads me to believe that it's the same for both ends. So area1 = area2. I am also only given a single weight (Which I convert to force by multiplying the weight by the accerleration of gravity). So basically the question is generalized as either the equation:
P = F / A
or
P = F * A

Answer 1

Pressure = Force / Area
Equations
Pressure In = Pressure Out
so
Force1 / Area1 = Force2 / Area2
and

Pressure1 = Pressure 2
so
Force1 * Area1 = Force2 * Area2

Are not conceptually the same equations, however marked differently (typo).

Let's say have a piston of radius R1 connected by a pipe L meters long to another piston R2 . Then you apply apply a force F1 to to the first piston what is the force F2 would the second piston experience?

Since we are dealing wit an incompressible fluid pressure at piston 1 will be the same as at piston 2.
P1=P2 and yes
P1=F1/A1
P2=F2/A2
so
F1/A1=F2/A2
and
F2= [F1/A1]A2
F2= F1[piR2^2/piR1^2]
F2= F1[R2/R1]^2

Also you may want to get the units straight if you are using SI units

Force -Newtons (N)
Area m^2( meters squared)
Pressure N/m^2 or Pascals (Pa)
_______________________________________
Can you please state the actual problem
It is definitely
P = F / A

Answer 2

The booklet is in error, perhaps a typographical error. Given the equation

F1/A1 = F2/A2 where F=force, A = area

Multiply BOTH sides by A1 to get: F1 = F2* A1/A2

Multiply BOTH sides by A2 to get F1*A2 = F2* A1

If you interchange the A subscripts in the formula in the booklet you get the above formula -- an easy typo for a type setter who doesn't know physics or math to make.

Shrikant R is in error. Consider a balloon.. Everywhere inside the balloon the air PRESSURE is the same. If it was not, the places where the air pressure were greater would be poking out further than the surrounding area. The surface of a balloon is smooth when inflated.

Consider a bicycle tire. Its is relatively easy to pump air into the tire with a hand pump because the valve stem where the air goes in has a small diameter which has a very small area compared to a square inch.

If the air pressure is 30 pounds per square inch inside the tire (each square inch of the inside surfaces of the tire have 30 pounds of force pushing against it). If the diameter of the valve stem is 0.25 inch, its area is: Av = PI * diameter ^2 / 4 which would be only about 0.049 square inches.

When you are pumping it up you are only pushing against a very small area compared to a square inch so the force you apply can be small, about 1.47 pounds (30 lbs/square inch * .049 square inch = 1.47 pounds of force). The units 'square inch', one in the top and other in the bottom of the equation cancel out just like numbers of the same value would cancel).

Answer 3

It seems the booklet has made a mistake. What we always use is
pressure=force/area
Check the booklet again, maybe it's:
force1*area2=force2*area1

Answer 4

If the pilots did no longer could desire to exert tension, there'd be no thank you to regulate the plane. Hydraulic structures in simple terms help the pilots, as a fashion to make it much less tense to go the administration surfaces. They nonetheless could desire to exert tension on the controls, and in the event that they choose severe strikes, they could desire to exert severe pressures. interior the Alaska airways case, the pilots have been attempting to counteract the entire tension of the stabilizer with trim jammed against the stop (without fulfillment), so they had to tug plenty extra sturdy than regular.

Answer 5

There should not be any confusion at all
Force1 / Area1 = Force2 / Area2 is not the correct formula.
you are getting the confusion with pressure & force.
FORCE = PRESSURE X AREA.
FORCE1 = PRESSURE1 X AREA.1
FORCE2 = PRESSURE2 X AREA.2
PRESSURE1 X AREA2. = PRESSURE2 X AREA2
HENCE
FORCE1 = FORCE2

Units we can put in metric as under

Pressure in Kg/cm2
Area In cm2
Then Total force applied will be in Kg

Answer 6

P = F/A
F = P x A
A = F/P