That is not a solvable problem as presented. At the point where the two systems meet the pressure will be the same or you need to throttle your 2" line down to meet the 3 psig limit or to limit flow to 10,000 lbs/hr.
If you're looking at a current 8000 lbs per hour? at 3 psi and you're going to add a further 10,000 lbs/hr, your total flow rate more than doubles, so your pressure drop will go up by a factor of about 4. however this then reduces the actual velocity of the steam and so you're probably looking at about double the current pressure drop, but simple to do a calculation using some proper steam software pressure drop calcs. Now it then depends if your supply of steam in the 8" line can cope with the increased back pressure or not. However your 2" line must somehow be controlled to 8000 lbs otherwise it will become open ended and reach near sonic velocity and lot more than 10,000 lbs/hr.
Try sketching this out so we can see what you mean then revert.
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