Can prove that you always gain in jet blocks by having smaller jet diameters and more jets, than less.
The main factor of trade off between back pressure and performance is the jet plate spacing parameter (how far the jet exit is for the base).
I believe Incropera and DeWitt suggest (heat transfer book highly recommended,
http://www.amazon.com/gp/product/047...Fencoding=UTF8) suggest for turbulent jets i.e. air jets (Re > 2000, think G7 is of order Re=100. so jets at exit from the nozzle do not have turbulent velocity components) that optimal spacing for parallel flat plates where the top one has holes in it to create jets is 5*D (where d is jet diameter). The optimal spacing of the jets in a square grid arrangement is 3 d’s apart. This will not be the case for water but it gives you an idea of the numbers we are talking of and that there is a maximum.
Jets not far enough apart interfere with each other and there is lower jet velocity (probably dominating factor) as mass flow rate is conserved
Mass flow jet = mass flow total / number of jets.
If the jets are too far apart cooling performance declines far away from directly below the nozzle performance declines.
High plate spacing and the jet starts to break down by friction with fluid (5D’s is high for a water jet, think it is more like 1D for water but just speculating).
Low plate spacing and performance does rise (can achieve spectacular heat transfer coefficients per unit area) but pressure drop also increases as the jet impacts the base plate and changes the direction quickly.
Pressure drop could probably be calculated for a single jet by a analytical solution of the Navier Stokes equation but you would need a degree in engineering and about 20 sides of a4 to do it properly. Multiple jets also muck it up some what. Expelling spent (heated up water) is hard and a major problem with jet designs.
NB most jet systems I have seen use a plenum (is that the right word?) where the nozzle tube is large till the end where it exits through a very small hole (dia tube about 3 times larger than hole I think sometimes 10 but these are wild guess of fuzzy memories). This minimises nozzle pressure drop and results in different flow properties.
Water exiting the hole is now un-developed (velocity across the diameter is flat) and you don’t get the pressure drop from the flow developing.
If you have a nozzle tube of over 10 dia’s then the flow is fully developed (has an x^2 distribution ie
Ujet(r) = Umax(1-k*r^2). Velocity is 0 at the walls according to classical theory. K is a constant of some sort
Because jet centreline velocity is now faster you get an increase in performance of about 5% BUT the pressure drop to achieve this is not worth the pay off.