# Determine the diameter of a piston

1. Nov 19, 2016

### skrat

1. The problem statement, all variables and given/known data
Determine the diameter of a piston if the working stroke of a piston is $h$ and if a working cylinder $(720^\circ )$ describes the following $p(V)$ diagram, where on the $x$ axis is a ratio between the current volume of a piston and the total volume (swept + clearance volume). The compression rate is 7.5:1.

2. Relevant equations

3. The attempt at a solution
I was able to calculate the height of the clearance volume (assuming it has the same shape as swept volume) by the following equation $$\frac{V_{clearance}+V_{swept}}{V_{clearance}}=7.5$$ so $$a=6.5 h.$$ And I honestly tried to calculate the diameter but everything I do leads me only to a ratio of some volumes, ergo the diameter falls out of the equation. I simply don't have an idea how to calculate the diameter of a piston.

2. Nov 20, 2016

### haruspex

I see your difficulty. It makes no sense to me either.
Btw, I believe the given h is Vswept, so your a = 6.5h is backwards.

3. Nov 21, 2016

### skrat

I apologize, I misread the problem statement. The swept volume $V_{swept}$ is also given. In that case, this is all a trivial problem.