Using the equation for terminal velocity, integrating the pull of gravity and air density, and using a Cd around 0.0006 (about what a thin, guided rod would have - typical for an arrow) I get a terminal velocity that is really high - around 31,000 meters per second. Is that reasonable? Well, there is essentially zero cross section, a lot of mass, zero drag, low air density for most of the flight, and lots of distance for gravity to work over...
Sanity check: most meteorites strike around 17,000 m/s so given we're quite a bit more aerodynamic than a meteorite, it's not all that unbelievable.
One kiloton of TNT is about 4.2 gigajoules, which is a lot smaller than your number (which seems to be about 1000 times too high). Run it all, and you're around 11-12 kilotons of energy.
Unless I'm off somewhere!
Aw, come on, how many of us has not done that a few times?
No way I would post any calculation unless I wrote it all out and triple checked it.
Meteorites may hit the upper atmosphere at 17000 m/s, but they sure don't hit the ground at that speed. And your tungsten pole is coming from orbit, not deep space, so it starts out at orbital velocity, about 8000 m/s.
Gravity will buy you a little coming from orbital altitude, but not 24,000 m/sec, and especially not 24,000 m/s through the atmosphere. A terminal velocity, at the earth's surface, of 31,000 m/s (that's 69,000 miles/hour, faster than *any* manmade object has *ever* gone, by a factor of almost two) ... that's completely impossible.
A kiloton is equal to 4.184 TERAjoules, not gigajoules. (It's in your link.)
So, if the rest of your calculation is correct, that's 11 or 12 tons of TNT, which would place in the upper range of conventional aerial bombs.