The stock steel trans lines are 5/16". they should also have a flare or bubble near the end to help hold the hose on and help seal when a clamp is applied. As Al suggests above, use fuel injection hose clamps as they seal all the way around the hose and don;t distort as much as when tightening. You may also have 3/8" hose going to the cooler, and that is probably never going to stay sealed on these 5/16" lines very well. I would check that and make sure the hose is not 3/8". Some aux coolers come with 11/32" hose so the hoses can be made to work with 5/16 or 3/8" metal lines, but 5/16" hole will still seal better on the metal lines. If the ends of the metal lies have been cut off and there is no longer the the flare or bubble there, you can go to a hardware store and get brass "compression to hose barb" fittings to adapt the lines. I used these on my power steering metal lines so I could route hoses up to a cooler mounted behind the grille. You can see these fittings at the end of ps cooler lines in the photo. You can also see the fuel injection hose clamps on the trans cooler hoses.
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