Window Channel
This one is 20 inches measuring the steel channel. The only part numbers are 1930 and I believe BS 1.
Thanks for your post! This window balance reminds me of the S350-20. Like yours, it has a wingless top and winged bottom shoe. The shoe should have a 1-3/32 depth (front to back measurement).
The 1930 should likely be the same. A pair of these will support a sash weighing 12 to 14lbs.
It would also be a good idea to double check that the windows have top sash guides in them. If these are damaged or missing, you will not be able to properly install the balances. Please see the tutorial below for reference.
If you are in need of a replacement for the top sash guides, please provide a photo of an undamaged guide, from a front-facing view.