# Calculating force of hydraulic cylinder

CognitiveNet
I want to calculate the force generated (as a result of expanding air) from pressure created by heating air up to a maximum temperature of 800 degrees Celsius.

My flywheel with a radius of 0,030m is rotating at a speed of 850RPM and weights 0,27Kg.
Angular velocity: w=850RPM*(2pi/60)=89rad/s
Moment of inertia of the flywheel: I=0,5*m*r^2=0,5*0,27*0,030^2=0,0001215 kgm^2
Kinetic energy: Ek=0,5*I*w^2=0,5*0,0001215*89^2=0,48N

Now I use Thermodynamics to calculate the supplied heat.
The room temperature is 20 degrees Celsius and the piston is 0,020m in diameter.

Area of piston: pi/4 *d^2=pi/4 *0,020^2=pi*10^-4
Force acting on piston due to the pressure inside the cylinder: F=P*A
I'm assuming this force is equal to the kinetic energy stored in the flywheel.
Thus P=F/A=0,47N/pi*10^-4=1527Pa
P1*V1/T1=P2*V2/T2
(Excluding the volumes because I just care about the initial kinetic force)
Pa = Normal atmospheric pressure at 20 degrees Celsius (or 293 Kelvin)
Thus T2=P2*T1/P1=1527Pa*293K/101300Pa=4K IMPOSSIBURU!

But the supplied heat is at least 800 degrees Celsius.
Assuming all of the heat is transferred into the air inside the cylinder, that's equal to 1073K.

Please tell me what's going on here. I have the feeling that I don't know how to calculate how much force the air is acting on the piston, as a result of an increase of pressure due to the increase of temperature.

## Answers and Replies

Science Advisor
Homework Helper
Kinetic energy: Ek=0,5*I*w^2=0,5*0,0001215*89^2=0,48N
Your units are not correct. Energy has the dimension of Force x distance and units in MKS are Joules.

Now I use Thermodynamics to calculate the supplied heat.
The room temperature is 20 degrees Celsius and the piston is 0,020m in diameter.

Area of piston: pi/4 *d^2=pi/4 *0,020^2=pi*10^-4
Force acting on piston due to the pressure inside the cylinder: F=P*A
I'm assuming this force is equal to the kinetic energy stored in the flywheel.
This is also dimensionally incorrect. Force cannot equal energy.

You have not explained the problem very well. Perhaps if you explained exactly how the piston is connected to the flywheel, we might be able to help you out.

AM

CognitiveNet
Your units are not correct. Energy has the dimension of Force x distance and units in MKS are Joules.

This is also dimensionally incorrect. Force cannot equal energy.

You have not explained the problem very well. Perhaps if you explained exactly how the piston is connected to the flywheel, we might be able to help you out.

AM

It's a Lamina Flow Stirling, or a thermodynamic stirling.