/fluid-systems

name: pie-fluid-systems
version: 1.0.0
description: "Water-based fluid system design: pipe sizing (Darcy-Weisbach, Hazen-Williams), flow rates, pressure drops, CDU selection for DTC cooling, pump curves, and ASHRAE TC 9.9 water class enforcement. Activates for cooling loop design, plumbing calculations, CDU selection, pump sizing, and hydraulic system validation."
user-invocable: true
allowed-tools: Read Grep Glob Bash
metadata:
  extensions:
    gsd-skill-creator:
      version: 1
      createdAt: "2026-02-26"
      triggers:
        intents:
          - "pipe sizing"
          - "flow rate"
          - "pressure drop"
          - "CDU"
          - "direct-to-chip"
          - "cooling loop"
          - "pump selection"
          - "NPSH"
          - "Darcy-Weisbach"
          - "Hazen-Williams"
          - "water cooling"
          - "hydraulic"
          - "plumbing"
          - "chilled water"
          - "ASHRAE"
        contexts:
          - "data center cooling design"
          - "plumbing system design"
          - "infrastructure engineering"
          - "cooling loop sizing"
applies_to:
  - skills/physical-infrastructure/**
  - "*.calc"
  - "*.pid"

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 |