# Using volumetric pressure to counter a force

1. Aug 28, 2015

### TaylorTexas

1. The problem statement, all variables and given/known data
There are two opposing cylinders, C1 and C2. Each cylinder is sealed. Each cylinder has a movable piston at one end. The pistons of each cylinder face each other. The pistons are connected to each other by a straight Shaft. C1 is connected to an air supply with an initial air pressure of 150 psi. Over time, the air pressure in the air supply, and thus C1, is increased to 157 psi.

The dimensions of C1 is .5" radius and 5" length. the initial air pressure in C2 is 150 psi. What are the dimensions of C2 (Length and Radius), to allow the Shaft to move 4" in the direction of C2 as the pressure increases 7 psi in C1, with a minimum of volume?

2. Relevant equations
I have used Boyle's law for two cylinders: P1V1=P2V2

3. The attempt at a solution
As the pressure increases in C1, the shaft begins to move right, decreasing the volume, and increasing the pressure in C2. When the shaft moves 4", the pressure in C1 and C2 are equalized and the shaft movement stops.

P1V1=P2V2
Inserting V=π * r12 * h1, I get
P1(π * r12 * h1)=P2(π * r22 * h2)
Where P1=157, r1=.5", h1=5, P2=150, r2=.4, I solve for h2.
Thus, h2=8.1.
So, I would need C2 to be 8.1" long and .4" radius to allow 4" of shaft movement with a change of 7 psi in C1?

#### Attached Files:

• ###### cylinders.jpg
File size:
10.9 KB
Views:
55
2. Aug 28, 2015

### paisiello2

I think you have mistakenly applied Boyle's law to two different gases in two different cylinders?

3. Sep 5, 2015

### Staff: Mentor

As paisiello2 has pointed out, this does not seem correct. Boyle's law relates the pressure and volume of a fluid in a single cylinder (or other confined fluid) before and after some process takes place, provided that the temperature of the fluid does not change. It does not relate the pressure and volume in two different cylinders (or other separate quantities of fluid).

4. Sep 5, 2015

### Staff: Mentor

A key assumption has been left out of the problem statement: that the temperature of everything stays the same. I'm assuming that was the intent; otherwise everything gets a lot more complicated.

That last qualifier, "with a minimum of volume", is important. Is that an exact quote? Is the intent that there should be a minimum change in volume in cylinder C2, or that cylinder C2 should have the minimum possible total volume at the end, consistent with the other quantities in the problem?

Yes, this looks correct.

Yes, this looks ok so far. But the next step is key: if the shaft moved 4 inches, what does that tell you? Specifically, what does it tell you about cylinder C1?