Chilled Water Header Pipe Sizing

A relatively crude way to do this is to use a rule of thumb such as water velocity = 3 m/s or 10 ft/s. A better way is to assess the length of the header and the acceptable pressure drop; and then use the Darcy-Weisbach or other commonly accepted formula. The research is left as an exercise for the reader.

Two issues to consider-

FIRST- Using just calculated velocity assumes that ALL the water is moving at the same velocity. In actuality, water at the center of the pipe is moving the fastest and gradually slowing until the water touching the inner pipe walls is "barely" moving relative to all the other water.

If you don't have a copy of the Crane "Flow of Fluids- Technical Paper 410", GET ONE. This book is the compilation of several years of testing of flow of fluids (compressible, incompressible, volatile, stable, etc.) in a wide variety of conditions. It includes ALL necessary formulas, and their derivation. It is comparable to "Fan Engineering" by Buffalo Forge (another "must have" book for serious engineers) in the massive amount of data and compiled knowledge that it contains.

Taking a short cut and going to the "Engineering Data" appendix, water flow of 20,000 GPM (the highest tabulated value presented) in a 24-inch Sch 40 pipe yields a defined pressure drop of 1.12 PSIG (or about 2.43 feet) per 100 feet at an mean velocity of 15.96 FPS. The same pressure drop in a 20-inch pipe yields a flow of 12,324 GPM and a velocity of 14.22 FPS. So, the same pressure drop yields a 63.4% increase in flow with a 12.2% increase of velocity by moving from 20-inch to 24-inch pipe.

Extrapolating that forward, 45,000 GPM (225% of 20,000 GPM) should require a velocity of about 43.2% higher [(225% / 63.4%) X 12.2%] or 22.85 FPS to have a pressure drop of 2.43 feet per 100 feet. 45,000 GPM is also (45000 / 60) or 750 GPS. 750 GPS also equals (750 / 7.5 gallons per CuFt) or 10 CuFt/sec. 10 CuFt / sec moving at 22.85 FPS requires 756.2 SqIn of internal pipe area. 32-inch STD pipe has an internal area of 767.0 SqIn- a little better than the goal so lower pressure drop.

HOWEVER- it is very likely that your AHUs have 2-way valves and you will be using variable speed drives on the primary flow supply water pumps. Using a VERY conservative 75% average cooling load vs the peak 25,000 tons, your NORMAL flow rate will be 33,750 GPM which would yield a flow of 7.5 CuFt per sec. and a velocity of 21.1 FPS for an area of 614.2 SqIn. 30-inch STD wt pipe (very common size) has an internal area or 672 SqIn., so the net velocity at 91% of design will yield a pressure drop of about 1.8 feet per 100 feet at "normal" flow and a peak pressure drop of 2.9 feet per 100 feet at peak flow (still reasonable).

SECOND- Another solution to your problem, that will save energy, is to change your parameters. You have not stated the DeltaT of your CHW system, but- your flow rate of 9,000 GPM per chiller IMPLIES (5) 5,000 ton chillers running at 16F DeltaT (a common range in current system design) or 44F supply water and 60F return water.

By applying a primary-secondary approach (which you may already be using) AND using 2 of your chillers to "pre-cool" the return water (extract, cool and re-inject into the return main with one sub-main connected upstream of the second sub-main connection supporting the other 3 chillers) you can change the design DeltaT to 24F and reduce your total water flow to 30,000 GPM. The upstream sub-main would flow at 18,000 GPM and those two chillers would cool the total water from 60F to 50.4F.

The second sub-main would flow at 30,000 peak GPM (depending on how many chillers were required at 10,000 GPM per chiller) and cool the water from 50.4F to 36F, giving you the full 24F differential but staying "warm" enough to avoid the risk of tripping low temp sensors.

Assuming that you will have two-way valves at the AHUs, and variable speed pumping, you COULD drop the CHW mains to 24-inch STD weight (internal area is 424.56 SqIn vs 402.1 SqIn for Sch40 used in earlier calcs. At the anticipated AVERAGE load of 22,500 GPM the pressure drop would be about 2.8 feet per 100 feet and, at the 30,000 Peak GPM the pressure drop would be 5.0 feet per 100 feet- high but not extreme and certainly reasonable considering the significant capital savings from using 24-inch STD pipe for the primary main fabrication.

The upstream chillers would operate at higher-than-current design efficiencies due to the higher temperatures and the final three would be a little lower efficiency but would essentially cancel each other out. The BIG savings would be in pump energy (33% less water circulating AND via another avenue- Since your AHUs would be seeing colder water, they could supply cooler air- 48F vs 55F, allowing the fans to use 28% less air to supply the same amount of cooling.

Additionally, you could have even MORE savings by raising the room temperatures to 80F and using the cooler, dryer supply air to maintain 35% RH (80/35RH FEELS the same as 73/50RH) so you could send in 44% less air than normal (32F DeltaT vs 18F) AND reduce thermal transfer cooling load for abut 12-15% lower total cooling load (less cooling AND less supply water AND less airflow).