Vector Force Addition: Understanding Pressure and Force in Colliding Streams

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Suppose I have 2 streams of water (say like 2 garden houses) side by side. If they are both shooting out at a certain pressure say 20 PSI and, they cross paths at 45 degrees (i.e left stream points 45degree to right and right stream points 45 to left). can the pressure or force of the combined streams where they collide, result in a pressure or force increase to say 30 and with a dir'n straight ahead (cancel out direction leaning left/right)?? Am i thinking correctly here?
 
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Without answering the question, let me point out that while force is a vector, pressure is not. Pressure is the dot product of force and the area vector.
 
Ok, how about the resulting forces instead of pressure. So 20 Newtons and 20 Newtons at 45 degree combines to something like 30?
 
^ if they are both hitting a third body then yes, the net resultant will be greater (approx 30).

But I'm not sure how the fluid dynamics would work with the two streams hitting each other, for some reason i doubt there will be an increase in the waters velocity...