bishnu Posted September 3, 2004 Share Posted September 3, 2004 how would i calculate the velocity coming out of an air cannon in terms of pressure, volume,barrel length, area of barrel opening, k(coffecient of porpotionalityin -kv^2 for friction)? Link to comment Share on other sites More sharing options...
pulkit Posted September 3, 2004 Share Posted September 3, 2004 Draw the free body diagram for the shell being fired, calculate forces acting on it, get an expression for acceleration and integrate to get velocity. You would need a law governing pressure and volume of air inside the pressure barrel, Eg.PV= constt Link to comment Share on other sites More sharing options...
bishnu Posted September 3, 2004 Author Share Posted September 3, 2004 i wish it was that easy but since i have friction in it becomesmuch harder [math]f_{net}=f_{pressure}+f_{friction}[/math] [math]f=pa[/math] [math]f=p_iv_ia/(v_i+ax)[/math] that equals the force from the air cannon using the equation p_iv_i=p_fv_i and since the volume increases by barrel opening(andassuming theprojectile fits snug in the tube) andhow far it has been shotthrough the tube [math]a=p_iv_ia/m(v_i+ax)-kv^2/m[/math] [math]y''=p_iv_ia/m(v_i+ay)-ky'^2/m[/math] but when i solved this diff equation i got obviously wrong equation maybe i just did the math wrong i dont know. i dont even know if that would give the right answer Link to comment Share on other sites More sharing options...
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