Target flow, tube size, and head loss question

[tropostudio]

Working through the math for system flow, tube sizing, and head loss has me a bit stumped. I get the math and know that the formula for heat transfer is an, but here's an example that illustrates my issues:

Say I have a level in the house that has a 15,000 BTUh design load (99% design temp of -8 F in St. Paul, MN which shouldn't really matter for this discussion). Figure on 5 identical emitters, each rated to put out 3,000 BTUh at 140F supply temp to heat the space. Assume Delta T of 30F. f = Q/500 x (∆T) gives a target flow rate of 15,000/500*30 = 1 gpm for the entire level, or 0.20 gpm per emitter.

Now its's time to pick tube size. Best practice suggests flow velocities between 2 fps - 4 fps.
v = 0.4084 f(gpm)/d (in) ^2. For a tube diameter of 0.5", this yields 0.4084 * 0.20 * 0.25 = 0.33 fps. Way too low. Tube diameter of 3/16" gets us to a flow velocity of 2.32 fps - right around the recommended low velocity limit to insure removing air bubbles, etc. That's a really small tube diameter., and the head loss would be ridiculous.

Now to head loss. Say I'm planning to set each emitter up as a home run off a manifold. My longest circuit is equivalent to 100 ft of 0.5" tubing. HL = k x c x L x f^1.75. Assume k of 0.04 for 1/" PEX-Al-PEX; c of 1.00 (close enough , for water at average temp of 125F); L = 100 ft; 0.20^1.75 = 0.06. HL = 0.28 ft. Very low, but my flow velocity is way too low. I can't find any values of k for 3/16" PEX, but say it existed and extrapolate from published values for available sizes. You'd have a k somewhere around 4, and doing the math gives a head loss of around 29 ft. Ridiculously high in order to achieve a flow velocity of 2.32 fpm.

I get that flow restrictors could tune the flow rate to a target flow of ~0.2 gpm at each emitter, but the flow velocity everywhere except through the restrictor will be too low.

What am I missing or where are my errors?

 

[tropostudio]

Seems like folks figure I'm in over my head on this, the question wasn't posed clearly, or nobody likes math. The first two for sure!

Anyway, I think I'm gaining an understanding of the situation. First I find the Target Flow Rate for each circuit based on BTUh requirements (Q) at that emitter at Design Temperature and Delta T. Add them up to get Total System Flow Rate. Check that across several Delta T's.

Now find the circuit with the largest Maximum Equivalent Length. If I decrease the Delta T for my the circuit, required flow goes up to satisfy Q. Now decrease pipe diameter to something commonly available until I get a flow velocity between 2-4 gps. I'm targeting 2 fps. Calculate head loss for that circuit. Check head loss at every circuit the same way using the same Delta T: vary pipe diameter to achieve 2 fps flow velocity. Now I'll know which circuit has the maximum head loss, and can pick a circulator(s) that will cover that envelope. With more circuits open, head loss drops and flow increases.

Can someone advise as to how critical it is to design for a minimum flow velocity of 2 fps at any circuit? If I use TRV's or proportional valves the flow velocity in the tubes will drop well below the value set for the circuit wide open. Is it it a matter of just insuring you get 2 fps sometimes to insure air bubbles move along?

I'm planning on a homerun system using TRV's at each emitter, or something very similar. One manifold per level (basement, 1'st floor, 2'nd floor). Will probably get by with 3/8" PEX-Al-PEX for each emitter; perhaps a couple using 1/2" PEX-Al-PEX and maybe even one or two with 1/4" PEX. Low-Medium loss Boiler like the Westinghouse WBRU, indirect hot water tank, ECM Delta P circulator such as Taco Viridian or Wilo ECO16, and panel radiators (mix of Myson T6 and Decor series, or equivalent). Can't post the calculations spreadsheet but a screenshot is attached.