## WARNING:

If you despise pushing buttons on a calculator, or looking at formulas, portions of this column might really annoy you (although probably not to the point of causing substantial property damage or death). The graphs at the end, however, will temporarily relieve the symptoms of formulaphobia.## A Fork In The Road:

Any heat emitter connected to a main piping circuit by one or two diverter tees represents an alternate path for a portion of the flow entering the upstream tee. The portion of total circuit flow that passes through the heat emitter depends on the flow resistance of both this branch path and the “main” path between the tees.The concept of “flow resistance” discussed way back in the February 1997 Hydronics Workshop column, is a good way to predict what happens in diverter tee piping systems. You’ll recall the basic idea of flow resistance is that each pipe, each fitting, valve, heat emitter or other component in a piping system can be given a resistance value based on how “restrictive” it is to flow. When all the piping components form a series circuit their flow resistances are added up to get the total resistance of the circuit. This in turn can be used to estimate the head loss of the piping circuit at any flow rate.

The two piping paths formed when diverter tees are installed represent parallel rather than series flow resistances. And just like parallel electrical resistors their individual resistances can be combined into a single equivalent resistance. The process is shown sequentially in Figure 1.

## What You Need To Know:

There are three things a designer needs to know about heat emitters connected in a system using diverter tee(s): First, what’s the flow resistance of the “diverter tee block” (formed by the tees, riser piping, control valve, main piping and fittings, as shown in Figure 1)? Secondly, how does the flow entering the upstream tee divide up among the two flow paths? And finally, what effect will gravity head have on branch flow rate? We’ll look at these one at a time.The head loss of each diverter tee block is needed to determine the flow rate a given circulator can sustain in the circuit. When several such diverter tee blocks are connected to form a series piping circuit, the flow resistance of each block can be added up along with the flow resistance of other piping components in the circuit to get the total flow resistance of the circuit. This lets you establish the system head loss curve, which in turn can be combined with a pump curve to estimate circuit flow rate.

The head loss of a diverter tee block is greatest when the control valve in the branch path is closed and thus no flow passes through the heat emitter. This happens because full circuit flow is pushed through the diverter tees which, by their design, create significant flow restriction. As the valve opens to allow flow in the branch path the resistance of the overall diverter tee block decreases. This means the flow rate in a circuit that contains several diverter tees will be greatest when all the branch paths are open.

You can find the flow resistance of each diverter tee block, (when the control valve in the branch path is fully open), by combining the parallel flow resistances R1 and R2 that represent the branch piping path and main piping path respectively as shown in Figure 1. When combined, their overall “equivalent” resistance is called Re.

You can get numbers for R1 and R2 by adding up the equivalent length of pipe and fittings in each piping path, and then multiplying by the factor in the far right column of Table 2.

Once you have these numbers plug them into Formula 1 to get the value of Re. To do this you’ll need a calculator that handles exponents.where:

Re = equivalent flow resistance of R1 and R2 R1 = flow resistance of the branch piping path (including risers, heat emitter, valve and fittings) R2 = flow resistance of the main piping path (including the main pipe and Monoflo® tees)

Note: The values -0.5714 and -1.75 in the formula are exponents, not multiplying factors. Calculate everything inside the square brackets first, then raise the result to the -1.75 power.

Example: Find the equivalent flow resistance of the diverter tee block shown in Figure 3:

Step 1: Add up the equivalent lengths of pipe, fittings and valves in each piping path.

Step 2: Convert each total equivalent length to a flow resistances using data from the far right column in Table 2 (for a specific pipe size).

R1= 45 x 0.0029 = 0.1305 R2 = 37 x 0.00032 = 0.0118

Step 3: Plug the values for R1 and R2 into Formula 1 and calculate:

The flow resistance of 0.00795 for this diverter tee block could now be added to the flow resistance of the other piping components in the circuit to establish the circuit’s system curve.

By the way, the value of Re will always be less than the smaller value of either R1 or R2 (whichever one is smaller). This is a way to partially check your calculations.

## Which Way Does It Go?

Once you know the circuit flow rate, the portion of it passing through the branch piping path can be estimated using Formula 2: where: fbranch = flow rate through the branch path (in gpm) fcircuit = flow rate in the distribution circuit (e.g. the flow entering the upstream tee) (in gpm) Re = equivalent flow resistance of the diverter tee block determined using Formula 1 R1 = flow resistance through the branch path
Note: The number 0.5714 is an exponent not a multiplier. First determine the value of the ratio within the brackets, then raise the result to this power.

## Example:

Assuming the flow rate in a piping circuit is 12 gpm, what’s the flow rate through the branch path in Figure 3. Answer: Plug in the numbers from the previous example and calculate:
The flow rate through the main pipe thus has to be 12 – 2.4 = 9.6 gpm.

## Formulaphobia:

If you like graphs better than formulas, Figure 4 is for you. To use it just calculate the ratio of the flow resistance in the main piping path (R2), divided by the flow resistance in the branch piping path (R1), then find this number on the lower axis of the graph, read up to the curve and over to the vertical axis to get the multiplier factor (M). The flow in the branch path equals the circuit flow rate times M.
If the flow resistance through the main path just happens to equal the flow resistance through the branch path, the ratio of R2/R1 is 1 and the multiplier factor equal 0.5. This means the flow divides up equally between the branch and main paths as your intuition probably predicted it would. If the flow resistance through the main piping is only 1/10 that through the branch, the branch flow drops to about 21 percent of the circuit flow. Most of the flow is predictably taking the easy path straight through the main. But if the flow resistance in the main is 10 times that in the branch, the branch flow is about 79 percent of that in the circuit. Again the majority of the flow takes the easier path between the tees.

## Don't Forget Gravity:

In the December 1997 column we looked at the effect of gravity head created by different temperature water in the two risers. When the heat emitter is above the main this gravity head actually helps move flow along the branch path (because water in the supply riser is warmer, and thus lighter, than water in the return riser. Warm water wants to go up, cool water wants to go down). But if the heat emitter is below the main the opposite is true. The latter case is where you have to be careful.The graph in Figure 5 shows the theoretical gravity head (expressed as equivalent feet of branch pipe) for a downfed riser system that drops 9 feet from the main to the heat emitter, with 180 degrees F water in the supply riser and 160 degrees F water in the return riser. This case was selected to represent a typical downfed baseboard. Once you know the approximate flow rate in the branch piping based on methods given earlier in the column, you can use this graph to estimate how many hypothetical feet of pipe to add into the branch path to account for gravity head effects. Then you can rerun the numbers, (or use Figure 4) to see how much the branch flow is effected.

Figure 5 indicates that when branch flows are “healthy” (say 4 gpm for 3/4 inch pipe, or 8 gpm for 1 inch pipe), the gravity head effect is insignificant (less than 1 foot of equivalent pipe length). But when branch flow rates are low, the gravity head effect working against them can become very significant. Bottom line: Low flow rates in long downfed risers can spell trouble. Given the conditions assumed the flow rate in a downfed 3/4 inch riser system should be kept at least 2.5 gpm, and in a downfed 1 inch riser at least 5 gpm in order to minimize the undesirable gravity head effect. Remember this graph only applies to the riser drop and water temperatures assumed. The greater the riser drop, and the greater the ³T between supply and return water, the more the gravity head effect works against branch flow. As if that weren’t enough, the temperature drop across the heat emitter increases as flow rate decreases further enhancing the gravity head effect. If you suspect weak flow in a downfed riser system play it safe and use two diverter tees.

If you’re designing a diverter tee block with an upfed heat emitter and a large vertical riser length, you may also want to use Figure 5 to estimate the equivalent feet of pipe to subtract from the branch piping path to account for gravity head effects. Remember, in this case gravity head actually helps the flow along. However, if you ignore this correction for upfed heat emitters you’ll still err on the conservative side. The flow in the branch piping path will likely be larger than what you estimated.

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