Pie Fluid Systems

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)

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

Pipe roughness epsilon:

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

C coefficients:

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

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:

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:

Typical DeltaT values:

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 GPM

At 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 in

Select 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):

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.

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

Surge pressure from sudden valve closure:

DeltaP_hammer = rho x c x DeltaV

Where c is approximately 1,400 m/s for water in rigid pipe. Keep surge pressure below the safety class limit (see Safety Boundaries).

Mitigation: slow-closing valves (5+ second stroke), surge tanks, relief valves, VFD-controlled pumps with soft ramp-down.

Data Center Cooling

ASHRAE TC 9.9 Water Classes

Class selection: Higher W class enables more free-cooling hours and lower PUE. Verify server inlet air temperature remains within ASHRAE A-class (15-35C) for mixed air+liquid environments.

Full ASHRAE TC 9.9 water class specifications -- @references/ashrae-tc9-9.md

CDU Selection for DTC Cooling

The Coolant Distribution Unit (CDU) is the heat exchanger that isolates facility water from the server-level coolant loop.

Sizing: CDU rated kW >= rack peak heat load x 1.25 (design margin)

Direct-to-chip (DTC) parameters:

Leak detection requirements:

Secondary containment: Drip pan beneath each rack assembly minimum for data center class. Guttered containment for high-density installations.

Full CDU selection criteria -- @references/ashrae-tc9-9.md

Pump Selection

Operating Point

The operating point is the intersection of the system curve (parabolic: DeltaP = k x Q^2) and the pump H-Q curve (from vendor data).

• Plot both curves on the same axes (flow rate vs head/pressure)
• Operating point must fall within the pump's stable operating region
• Avoid operating on drooping portions of the pump curve

NPSH Verification

Net Positive Suction Head prevents cavitation:

NPSH_available = (P_atm - P_vapor) / (rho x g) + z_source - h_friction_suction

Rule: NPSH_available must exceed NPSH_required (from vendor pump curve) by at least 0.5 m. Recommended margin: 1.0 m.

Low NPSH remedies: Lower pump elevation relative to source, shorten suction pipe, increase suction pipe diameter, reduce suction-side fittings.

Cavitation consequences: Noise, vibration, impeller erosion, loss of flow capacity, eventual pump failure.

Pump Affinity Laws (VFD Sizing)

VFD benefit: Reducing flow to 50% by reducing pump speed saves 87.5% of pump power. This is the primary justification for VFD on variable-flow cooling loops.

Redundancy Configurations

Switchover: Flow switch or differential pressure switch triggers automatic switchover within seconds. Lead-lag rotation distributes wear.

Full pump curve analysis and VFD selection -- @references/pump-selection.md

Safety Boundaries

Pressure and Temperature Limits by Safety Class

Safety Warden Integration

This skill produces CalculationRecord objects with safety margin calculations. The Safety Warden reviews these and generates SafetyFinding entries:

Industrial and data-center class findings with severity='critical' or 'blocking' always require PE review before construction.

Reference Documents

Fluid Systems Skill v1.0.0 -- Physical Infrastructure Engineering Pack Phase 435-01 | References: ASHRAE TC 9.9, ASME B31.9, HI (Hydraulic Institute) All outputs require verification by a licensed Professional Engineer.