# Energy Equations Driving Me Crazy

1. Aug 13, 2011

### GBT

Alright, so I'm trying to design an air camber for a paintball marker. I know to get an approximation for the volume I can use energy equations. I'm using:

KE1 + PE1 = KE2 + PE2
and
KE = .5mv^2
PE = pressure(volume)

I want an initial pressure of 150 psi, and a final velocity of 290 feet per second. A paintball's mass is approximatly 3.19 grams or 0.007 lb.

I set up an equation like this:

(150 lb/in^2)(X)=(.5)(0.007lb)(3480 in/s)^2

A friend said it was 6.4 in^3, but I can't see what he did.

I don't know if I've just done conversions wrong, set up the problem wrong, or what.

Last edited: Aug 13, 2011
2. Aug 14, 2011

### CDCraig123

3. Aug 14, 2011

### GBT

I apologize: .5mv^2 is one-half mass times velocity squared. Or (1/2)(mass)(velocity)^2 if that is easier to see.

I realize that KE1 would be zero, and PE2 should be able to be ignored as well.

4. Aug 14, 2011

### CDCraig123

I think you are missing a term in potential energy. Maybe gravity ?

5. Aug 14, 2011

### ironic

I found the following info, it might be of help for your calculations:

We know that 1.8 grams of CO2 == 61.02in3 so (12/1.8)(61.02)=406.7Vin3 at 1atm
We know that 1atm == 14.7 PSI so (406.7) * 14.7 / 150 = 39.86in3
So 12 grams of CO2 will fill 39.86in3 at 150 PSI at 77F.

Calculating the velocity:
V²rms = 3RT/M; where M is molecular mass in kg/mole and R is the gas constant with the units 8.314 J/mol K. These unusual units are used because we want the answer in m/s, and by definition, 1 joule equals 1 kg*m²/s². The molecular mass of CO2 is 44 g/mol, or 0.044 kg/mol.
The calculation on this:Vrms = √[(3) (8.314 J/mol K) (280 K) / (0.044 kg/mol)]
Vrms = 398.4 m/s. So the speed of molecules at 280K is 398,4 m/s.

You would need to calculate the loss due through friction (length pipe)
and the inertia of your paint ball.

good luck

6. Aug 14, 2011

### GBT

The potential energy of a fluid can be expressed as the pressure times the volume if I'm not incorrect.

I'm going to use compressed air not co2, so I'm looking for the needed volume of air in a holding chamber at 150 psi (my desired pressure), that will propel a paintball up to 290 feet per second.

7. Aug 14, 2011

### ironic

Ok, did'nt catch up that your using air.
Perhaps you don't need much more for calc the velocity by changing the mol weight?