[wdfifteen]

Is this "pipe" emt (conduit)? Seems like you could use that for the ground, assuming it has a good bond all the way back to the box. In a commercial job I did I was required to bond all the device boxes to the EMT and they tested for continuity all the way to the breaker box. Most of the runs were FMC (flexible metallic conduit). It passed inspection, so I assume it is NEC compliant. I would definitely make sure you have good connections all along the run.

Our new electric clothes dryer came with instructions on how to connect it to 3-wire service. Red to hot, Black to hot, white to neutral, and a jumper from the frame of the dryer to the same lug the white wire is on.