How much mass per sec per Saturn V engine: efficiency discussion

Seventh in the series on Hunter gas guns.  The sixth is here.

According to Wikipedia, the fuel pump produced 58,564 litres of RP-1 every minute, which translates into about 791 kg/sec for the fuel.  For the oxidizer, 93,920 liter/min which equals 1565 liter/sec, which translates at a density of 1.141 g/ml to 1786 kg/sec.  Taken together, this adds up to 2577 kg/sec reaction mass.  To convert that to pounds, multiply by 2.2 giving  5569 pounds/sec.  From this, each of the five Saturn V engines produced 1,500,000 pounds of thrust.

The ratio of mass of the fuel to the thrust is 269.  That means, by heating the fuel and running it out the nozzle magnifies its force over gravity by 269 times.  The purpose here is that I want to understand how rocket engines work so as to understand why they use as much energy as they do in order to do the task assigned to them.  It still amazes me how much energy they do use.  I thought I was on to some sort of understanding, but it all went to smash.  I figured that it was exhaust velocity times its mass yielding kinetic energy, and it was the kinetic energy that did the work.  But these numbers don't add up to that conclusion.  Or I'm missing something.  Come to think of it, I am missing something because an explanation given here shows that I'm on the right track, basically.

It seems my calculations may be wrong somewhere.  Okay, that messes things up a bit.  Well, it's all a learning experience.  I made a mistake, darn it.  The thrust calculations for the gas gun are too high because I didn't account for the gravitation constant ( I think).

Are the numbers realistic for the energy claims I saw earlier?  It must be true because it was listed in two different places.  These things are energy hogs, no question about it.  That's still right.

Rockets must use energy in a much different way that a gasoline engine does.  A comparison in energy efficiencies shows that a gasoline powered internal combustion engine is much, much more efficient in terms of energy.  It is not usually understood that way.  That is, auto engines are thought to be quite wasteful of energy.  But not compared to rockets.  Compared to rockets, they are a picture of efficiency.

Try to imagine using a rocket engine to get around instead of an internal combustion engine.  You couldn't afford it.

I think a gas gun could be more like an auto engine.  The gas gun is making the gas do work before it is exhausted out the system.  I'm thinking that the rocket engine's exhaust doesn't do work and that's why it is inefficient with energy.

Why would gas guns be any better than rockets?

With a rocket, you have to carry your fuel around.  But a gas gun does too.  But with the gas gun, the acceleration is applied to the mass without it carrying the fuel along with it, or so I think.  Or it is because it makes more efficient use of the energy somehow?  The rocket fuel when burned doesn't do much work.  It just accelerates its own mass which is then sent out the nozzle.  For this reason, a rocket is said to be a reaction engine, based upon Newton's Laws of Motion.  But the same thing can be said of the gas gun.  It is also producing an action-reaction sequence itself.

So, is the gas gun any better than rockets?  I'll have to look at my corrections and see if it actually is.  I thought so before, but now, I'm not so sure.

Update:

This may not be related, but I'm including it anyway.  The thrust for the lunar module ascent stage was only
3500 lbf.  This does not seem like much, ya know?

Update:

The equation to calculate thrust.  Thrust equal isp*g0*mass flow rate.  The mass flow rate is approximated above.  Isp is from the engine specs, g0 equal gravitation constant.

The numbers almost check out, but not quite.