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.

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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")

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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 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):

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.

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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

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.

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Data Center Cooling

ASHRAE TC 9.9 Water Classes

Class	Supply Temp Range	Typical Use Case	Economizer Hours/Year
W1	2-17C	Legacy data centers, high-density GPU	<500 (most climates)
W2	2-27C	Mixed air + liquid cooling	~500-2,000
W3	2-33C	Modern liquid-cooled, moderate climates	~3,000-5,000
W4	2-45C	Warm water cooling, high economizer use	~6,000+
W5	>45C	Hot water, heat recovery to district heating	~8,000+

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:

Parameter	Typical Range	Notes
Flow per cold plate	0.5-2.0 LPM	Verify with server/GPU vendor spec
Server-side pressure	50-150 kPa	CDU provides pressure isolation
Cold plate inlet temp	25-45C (W3/W4 class)	Depends on water class
Manifold topology	Per-rack supply/return headers	Quick-disconnect fittings

Leak detection requirements:

Zone	Sensor Location	Response
1 - Server tray	Overflow tray in each tray	Local alert
2 - CDU drain pan	Under each CDU assembly	Auto-shutoff CDU supply
3 - Raised floor	Floor-mounted leak cable/sensor	Room alarm + facility shutoff
4 - Building BMS	Aggregated from all zones	Facility-wide response

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

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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

Condition	P_vapor (kPa)
Water at 20C	2.34
Water at 40C	7.38
Water at 60C	19.9
Water at 100C	101.3

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)

Parameter	Scaling Law	Example (50% speed)
Flow Q	Q2 = Q1 x (N2/N1)	50% flow
Head H	H2 = H1 x (N2/N1)^2	25% head
Power P	P2 = P1 x (N2/N1)^3	12.5% power

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

Configuration	Description	When to Use
Duty/Standby	Two pumps each at 100% capacity; one runs, one standby	Critical single-loop systems
N+1	N duty pumps + 1 standby with lead-lag rotation	Multi-pump parallel systems
2N	Fully redundant parallel systems	Highest criticality (Tier IV)

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

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Safety Boundaries

Pressure and Temperature Limits by Safety Class

Parameter	Residential	Commercial	Data Center	Industrial
Max working pressure	80 PSI	150 PSI	150 PSI	300+ PSI (PE required)
Max supply temperature	60C	82C	55C (server side)	150C+ (PE required)
Leak containment	Drip pan	Sensor + shutoff	Sensor + shutoff + alarm	Engineered containment
Pressure testing	Visual inspection	Hydrostatic 1.5x MAWP	Hydrostatic 1.5x + leak-down	Per ASME B31 code section
Water hammer limit	Not calculated	25 PSI spike max	10 PSI spike max	Per surge analysis

Safety Warden Integration

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

Condition	Severity	Domain	Action
Calculated pressure > safety class max	blocking	pressure	Requires human review (PE)
Temperature > safety class max	critical	temperature	Flag for PE review
NPSH_available < NPSH_required	critical	pressure	Cavitation risk -- redesign suction
Missing leak detection (data-center class)	warning	containment	Recommend sensor installation

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

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Reference Documents

Reference	When to Read	Coverage
@references/pipe-sizing.md	Detailed Darcy-Weisbach derivation, Moody chart, Colebrook equation	Full pipe hydraulics theory
@references/ashrae-tc9-9.md	Full ASHRAE TC 9.9 water class specifications, CDU selection criteria	Data center cooling standards
@references/pump-selection.md	Pump curve analysis, NPSH calculation, VFD sizing, affinity laws	Pump engineering

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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.