Fluid Systems Skill
At a Glance
Design and validate water-based fluid systems from household plumbing to high-density data center cooling loops.
Activation: InfrastructureRequest type='cooling' or type='plumbing', any CDU sizing request, pipe sizing question, flow rate calculation, or pressure drop analysis.
Key capabilities:
- Pipe sizing via Darcy-Weisbach (all fluids) and Hazen-Williams (water only)
- Flow rate calculation from heat load (Q = Q_heat / (rho x Cp x DT))
- Pressure drop analysis with fitting equivalent lengths
- ASHRAE TC 9.9 water class selection (W1-W5) for data center cooling
- CDU/DTC cooling selection and manifold topology
- Pump curve analysis with NPSH verification and affinity laws
- Safety boundary enforcement by safety class (residential through industrial)
ENGINEERING DISCLAIMER: All calculations must be verified by a licensed Professional Engineer before use in construction or installation. Local plumbing codes (IPC/UPC) and pressure vessel standards (ASME B31.9) impose requirements not captured here. User assumes all responsibility for verification.
Quick routing: Pipe sizing method -- see Pipe Sizing. ASHRAE water class selection -- see Data Center Cooling. Pump selection and NPSH -- see Pump Selection. Full derivations -- @references/pipe-sizing.md.
Pipe Sizing
Darcy-Weisbach (All Fluids)
The general pressure drop equation for incompressible flow in pipes:
DeltaP = f x (L/D) x (rho x v^2 / 2)| Variable | Definition | Units | |----------|-----------|-------| | DeltaP | Pressure drop | Pa | | f | Darcy friction factor | dimensionless | | L | Pipe length | m | | D | Internal pipe diameter | m | | rho | Fluid density | kg/m^3 | | v | Flow velocity | m/s |
Friction factor f: Determined from the Moody diagram or computed via the Colebrook-White equation for turbulent flow:
1/sqrt(f) = -2 log( epsilon/(3.7D) + 2.51/(Re sqrt(f)) )This is implicit in f and requires iteration (3-4 iterations from f=0.02 starting point converge). The Swamee-Jain explicit approximation avoids iteration -- see @references/pipe-sizing.md.
Reynolds number: Re = rho x v x D / mu
| Regime | Re Range | Friction Factor | |--------|---------|-----------------| | Laminar | < 2,300 | f = 64/Re | | Transition | 2,300 - 4,000 | Avoid -- unstable | | Turbulent | > 4,000 | Colebrook equation |
Pipe roughness epsilon:
| Material | epsilon (m) | Common Use | |----------|------------|------------| | Copper | 0.0000015 | Plumbing, chilled water | | PVC | 0.0000015 | Drain, low-pressure supply | | Galvanized steel | 0.00015 | Older installations | | Cast iron | 0.00026 | Municipal, fire protection | | Stainless steel | 0.000015 | Process, high-purity |
For full Colebrook equation derivation and Moody chart interpretation -- @references/pipe-sizing.md
Hazen-Williams (Water Only)
Simpler empirical formula valid only for water at normal temperatures in turbulent flow:
v = 0.849 x C x R^0.63 x S^0.54| Variable | Definition | Units | |----------|-----------|-------| | v | Velocity | m/s | | C | Hazen-Williams coefficient | dimensionless | | R | Hydraulic radius (D/4 for full circular pipes) | m | | S | Slope of hydraulic grade line (DeltaP / (gamma x L)) | dimensionless |
C coefficients:
| Material | C Value | |----------|---------| | Copper | 150 | | PEX | 150 | | PVC | 150 | | New steel | 145 | | Cast iron | 130 | | Old steel (20+ years) | 100 |
When to use: Water systems only, turbulent flow, not valid for viscous fluids or non-circular pipe cross-sections. Simpler than Darcy-Weisbach but less accurate; acceptable for plumbing design and preliminary sizing.
Velocity Limits
| Application | Min (ft/s) | Max (ft/s) | Rationale | |-------------|-----------|-----------|-----------| | Main distribution lines | 4 | 6 | Balance pressure drop vs noise | | Branch lines | 2 | 4 | Noise reduction near occupants | | Data center cooling | 3 | 8 | Higher acceptable in enclosed space | | Suction piping | 1 | 3 | NPSH protection |
Velocities below 2 ft/s risk sedimentation; above 8 ft/s risk erosion, noise, and water hammer.
Standard Pipe Size Selection
Process: Calculate minimum internal diameter from velocity limits at design flow rate, then select the next larger NPS (Nominal Pipe Size).
Standard NPS sizes: 1/2", 3/4", 1", 1-1/4", 1-1/2", 2", 2-1/2", 3", 4", 6", 8", 10", 12"
Full OD/ID data available from engineering-constants.ts via getPipeSize(nps, schedule).
Schedule selection:
| Schedule | Use Case | Wall Thickness | |----------|---------|----------------| | Schedule 40 | Standard pressure (up to ~150 PSI for smaller sizes) | Standard | | Schedule 80 | Higher pressure, corrosive fluids | Thicker wall, smaller ID |
Metric equivalents: DN15 (1/2"), DN20 (3/4"), DN25 (1"), DN50 (2"), DN100 (4"), DN150 (6"), DN200 (8"), DN300 (12")
Flow Rate Calculation
From Heat Load
Primary formula for determining coolant flow rate to remove a given heat load:
Q_flow (L/s) = Q_heat (kW) / ( rho (kg/m^3) x Cp (kJ/(kg K)) x DeltaT (K) )Water properties:
| Condition | rho (kg/m^3) | Cp (kJ/(kg K)) | |-----------|-------------|-----------------| | Water at 20C | 998 | 4.182 | | Chilled water at 7C | 999.8 | 4.195 | | Warm water at 45C | 990 | 4.180 |
Typical DeltaT values:
| Application | DeltaT (C) | |-------------|-----------| | Data center primary loop | 8-12 (ASHRAE recommended) | | Server-side CDU loop | 5-8 | | Chilled water plant | 6-8 | | District heating return | 15-25 |
Unit conversions: 1 L/s = 15.85 GPM | 1 kPa = 0.145 PSI | 1 kW = 3,412 BTU/hr
Worked Example
Scenario: 40 kW rack, supply 20C, return 30C, DeltaT = 10C
Q_flow = 40 / (998 x 4.182 x 10)
= 40 / 41,736
= 0.000958 m^3/s
= 0.958 L/s
= 15.2 GPMAt 6 ft/s (1.83 m/s) target velocity:
A = Q / v = 0.000958 / 1.83 = 0.000524 m^2
D = sqrt(4A / pi) = sqrt(4 x 0.000524 / 3.14159) = 0.0258 m = 1.02 inSelect next larger NPS: 1-1/4" (Schedule 40, ID = 1.38 in). Actual velocity: 3.3 ft/s -- within acceptable range.
From Fixture Units (Plumbing)
Per UPC/IPC Table 610.3 (demand conversion):
| Fixture | Fixture Units (FU) | |---------|-------------------| | Water closet (flush valve) | 10 | | Water closet (tank) | 4 | | Lavatory (private) | 1 | | Lavatory (public) | 2 | | Kitchen sink | 2 | | Shower | 2 | | Bathtub | 4 | | Dishwasher | 2 | | Washing machine | 4 |
Demand conversion: Total fixture units mapped to design flow rate via UPC demand curve (not linear -- accounts for diversity). Approximately: 1 FU corresponds to 1 GPM demand basis at the riser.
Pressure Drop Analysis
Equivalent Length Method (Fittings)
Convert each fitting to an equivalent length of straight pipe, then sum with actual pipe length for total pressure drop calculation.
| Fitting | Equivalent Length (pipe diameters) | |---------|-----------------------------------| | 90 degree standard elbow | 30D | | 90 degree long-radius elbow | 16D | | 45 degree elbow | 16D | | Tee (flow through branch) | 60D | | Tee (straight through) | 20D | | Gate valve (fully open) | 8D | | Globe valve (fully open) | 340D | | Check valve (swing) | 50D | | Ball valve (fully open) | 3D | | Strainer/filter | 50-100D (check vendor data) |
System Curve
Total system pressure drop is the sum of all resistances:
DeltaP_total = DeltaP_pipe + DeltaP_fittings + DeltaP_equipment + DeltaP_elevation- Pipe losses: Darcy-Weisbach or Hazen-Williams applied to total equivalent length
- Equipment losses: CDU, chiller, heat exchanger -- use vendor pressure drop curves at design flow
- Elevation term: DeltaP_elev = rho x g x DeltaH (Pa), where DeltaH = height change in meters
- Design margin: Size system to operate at 75% of available pressure differential to accommodate future expansion
Water Hammer Check
Surg