Pump motor sizing

[LovinLife]

You'll have to pardon me for not being more knowing on this subject but I've been in the mechanical field so far. I'm having trouble figuring how much pressure and HP is needed to pump Dexron6 (transmission fluid) at a temperature of 14F, through a system with 3/4" I.D. hose. This is a closed-loop application with no reservoir. We are going through a cooling radiator just before entering part so this is where the coldest, highest viscosity, highest pressure, occurs. Half way through this loop the fluid enters and exits a part, thus cooling it. Entire circuit is no more than twenty feet in length. Pump will sit two to three feet below main circuit level with hoses entering and returning from the circuit on basically a 45 degree angle. The rate is 1.5 to 4 GPM (variable speed pump motor) with a viscosity of 196.6cSt (at 14F) but I'm not seeing any friendly formulas for converting this information to what I need.
Thank you for any help you can provide.

 

[BigInch]

Look up the Churchill formula. That's the easiest. You'll need the roughness of the hose. Don't forget to add head loss for fittings and bends.

You might also search for some head loss vs diameter tables for oils. Google this one "oil flow through pipe tables". I got some hits on that one. 2,3 & 4 might do the trick.

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