I need help with a gas expansion problem.
A pumpkin is put on a sabot ( approx. 10 kg total )
the sabot fits in a 250 mm diameter 3 metre long barrel.
The base of the sabot must be held a distance X from the end of the barrel, and the space under the sabot is then pressurised to 7 bar ( gage ) at 20 C
The sabot is released.... the pumpkin hopefully exits in a hurry.
I need to know how to calculate the exit velocity of the pumpkin to find the best value of X. To small an X and there is not enough air to propel the load, to large and there is not enough barrel left to accelerate the load.
P1 x V1 = P2 x V2 is not going to work, as energy is not conserved within the gas.
Is the state of the gas " charge " indeterminate for the problem as stated ? if so what additional information is required ?
Possibly significant factors that might complicate things are the gas mass, seal friction, and ambient temperature. If I have a simple model I can then see how important they are likely to be.
Once I have a prediction of the exit velocity I can work out how far I can fire the pumpkin... over 200 m would be nice :-)