title	AI-Native Data Center Pod - 10 MW Reference Architecture (PoC)
author	Antreas Christofi
date	2026-02-11
toc	true
toc-depth	3

Authority Model

BoD is the single normative source of requirements and evidence gates.
Appendices are the single source of derivations and worked examples.
Reference Architecture instantiates a topology that satisfies the BoD by reference only.
Witness excerpt is a pointer and reconciliation summary; the authoritative witness lives in Appendix F.

Engineering Basis of Design

Physics-First, Vendor-Agnostic

0. Executive Snapshot

Purpose:
Define a facility capable of sustaining ~10 MW IT load for large-scale AI training with liquid-cooled racks, while remaining safe, observable, and operable across its lifecycle.

What this document is

A set of engineering contracts between IT and facility
A definition of envelopes (power, heat, water, telemetry)
A framework for commissioning and evidence

What this document is not

A vendor selection
A construction drawing pack
A detailed controls implementation

System Chain (intent)

Workload → Electrical Power → Heat Capture → Fluid Transport → Heat Rejection → Monitoring → Operations

Key Envelopes

Domain	Target
IT load	10 MW nominal
Rack cooling	Direct liquid to chip + CDU
$\Delta T$ liquid	8–12 K initial assumption
Redundancy	N+1 at critical layers
Observability	Second-level telemetry

1. Scope, Audience, Definitions

1.1 Audience

Electrical & mechanical engineering
Controls & BMS teams
Safety/compliance
Operations

1.2 Boundary Definitions

IT boundary: rack manifolds and CDU interface
Facility boundary: power delivery, fluid loops, heat rejection, controls
Responsibility split defined at CDU inlet/outlet and rack PDU

1.3 Terminology

FW – facility water loop
TC – technical coolant to racks
CDU – coolant distribution unit
HIL – hardware-in-loop testing
KPI – sustainability & performance metric

2. Architecture Contracts (Normative Core)

A. Electrical Contract

The facility shall:

Deliver up to 10 MW IT power with defined ramp limits
Support dynamic AI workloads with bounded inrush
Provide:
- N+1 at MV/LV transformation
- Selective coordination
- Power quality monitoring

Evidence

FAT/SAT under staged load banks
Ramp tests 0→100% and 100→0%
Harmonics and THD reports

B. Thermal Contract

Capture ≥ 95% of IT heat via liquid path
Maintain rack inlet temperature within OEM envelope
Provide:
- Dual-loop separation (FW / TC)
- Leak containment and detection
- Minimum $\Delta T$ target 8 K

Evidence

Calibrated heat balance
Flow vs load linearity
CDU failover test

C. Water Contract

Water quality per OEM specification
Treatment for corrosion/biological control
Leak detection at:
- rack
- CDU
- header

Evidence

Lab analysis
Pressure decay tests
Containment verification

D. Observability Contract

All critical paths instrumented
Time-synchronized telemetry
Alarms classified:
- Safety
- Service
- Advisory

Evidence

Telemetry acceptance
Alarm storm testing
Loss-of-signal scenarios

E. Sustainability Contract

Measure PUE, WUE, CUE boundaries
Reportable metering at:
- utility entry
- IT PDUs
- cooling plant

Evidence

KPI reconciliation
Sensor calibration records

3. Reference Architecture Overview (Non-Normative Orientation)

3.1 Electrical

Utility → MV → LV
Static transfer where required
Rack PDUs with branch monitoring
Grounding and bonding strategy

3.2 Mechanical

FW loop to dry coolers
CDU layer with TC distribution
Residual air path for ancillaries

3.3 Controls

BMS + DCIM integration
State machines for:
- ramp
- fault isolation
- maintenance modes

3.4 Safety

EPO logic
Leak isolation
Fire strategy compatible with liquid cooling

4. Architecture Tradeoffs and Design Decisions

This section records the key architectural decisions made within the admissible physical envelope established in Appendices A–F.

The appendices prove feasibility.
This section explains selection.

Each decision represents a chosen operating point within a broader feasible region, balancing thermodynamic efficiency, reliability, operability, and deployment constraints.

4.1 Cooling Topology Selection

Decision
Warm-water direct-to-chip liquid cooling with CDU-mediated separation between facility water (FW) and technical coolant (TC).

Alternatives Considered

Air cooling
Rear-door heat exchangers (RDHx)
Full immersion cooling
Hybrid air/liquid approaches

Tradeoffs

Approach	Advantages	Disadvantages
Air cooling	Simpler infrastructure, mature operational model	Cannot sustain ≥100 kW/rack without excessive airflow, fan power, and acoustic burden
RDHx	Compatible with existing air-cooled hardware	Retains airflow dependency and heat rejection inefficiencies
Immersion	Excellent heat transfer and density potential	Operational complexity, hardware compatibility constraints, vendor coupling
Direct-to-chip (selected)	Highest heat capture efficiency, scalable to ≥150 kW/rack, vendor-neutral facility interface	Requires liquid infrastructure and leak containment

Rationale

Direct-to-chip liquid cooling maximizes primary heat capture efficiency while preserving hardware and operational flexibility.
It aligns with the ≥95% liquid heat capture contract and enables rack densities beyond the practical limits of air cooling.

The CDU separation preserves facility independence from IT coolant chemistry and hardware refresh cycles.

Sensitivity

If rack densities remained below approximately 40 kW/rack, air or hybrid cooling approaches could remain viable.
If immersion becomes operationally standardized across vendors, immersion may become favorable in future revisions.

4.2 Thermal Rise ($\Delta T$) Selection

Decision
Design liquid temperature rise of approximately 12 °C (envelope 8–15 °C).

Alternatives Considered

Low $\Delta T$ (5–8 °C)
High $\Delta T$ (15–20 °C)

Tradeoffs

$\Delta T$	Advantages	Disadvantages
Lower	Lower component temperature gradients, simpler control	Higher required flow rates, larger pipes, higher pumping power
Higher	Lower flow rates, smaller pipes, reduced pumping power	Reduced thermal control margin, potential component temperature risk
12 °C (selected)	Balanced flow rate, pumping power, and thermal margin	Requires coordinated control

Rationale

The selected $\Delta T$ minimizes hydraulic infrastructure size while maintaining sufficient thermal margin for control stability and transient absorption.

This choice reduces pipe diameter, pump sizing, and parasitic energy without compromising component safety.

Sensitivity

Lower $\Delta T$ may be required for hardware with tighter thermal tolerances.
Higher $\Delta T$ may be feasible with validated component envelopes and control authority.

4.3 Mechanical Fault Domain Size

Decision
Maximum mechanical fault domain size of approximately 1 MW.

Alternatives Considered

Smaller zones (250–500 kW)
Larger zones (2 MW or greater)

Tradeoffs

Zone Size	Advantages	Disadvantages
Smaller	Greater fault containment	Increased infrastructure complexity and cost
Larger	Reduced infrastructure overhead	Larger thermal impact during failures
1 MW (selected)	Balanced containment, manageable infrastructure complexity	Moderate additional infrastructure overhead

Rationale

A 1 MW zone size ensures that hydraulic or cooling failures remain locally recoverable without propagating to the full facility.

This aligns mechanical fault domains with operational recoverability and commissioning isolation.

Sensitivity

Higher availability targets may justify smaller zones.
Lower capital cost priorities may justify larger zones.

4.4 Electrical Fault Domain Size

Decision
Electrical distribution blocks of approximately 2 MW.

Alternatives Considered

Smaller blocks (≤1 MW)
Larger blocks (≥5 MW)

Tradeoffs

Block Size	Advantages	Disadvantages
Smaller	Better fault isolation	Increased electrical infrastructure complexity
Larger	Reduced infrastructure overhead	Larger blast radius during faults
2 MW (selected)	Balanced coordination, scalability, and fault containment	Moderate infrastructure overhead

Rationale

2 MW electrical blocks align with mechanical zoning while maintaining manageable switchgear and protection complexity.

This structure supports selective coordination and staged energization during commissioning.

Sensitivity

Higher grid instability environments may favor smaller blocks.
Highly stable utility environments may support larger blocks.

4.5 Heat Rejection Strategy

Decision
Primary reliance on dry cooling, with optional heat reuse as a secondary path.

Alternatives Considered

Mandatory heat reuse
Evaporative cooling primary systems

Tradeoffs

Strategy	Advantages	Disadvantages
Mandatory reuse	Maximum energy recovery	Introduces dependency on external heat consumers
Evaporative primary	High efficiency	High water consumption
Dry primary, reuse secondary (selected)	Independence, water conservation, operational robustness	Slightly lower peak thermal efficiency

Rationale

The facility must remain fully operable independent of external heat consumers.

Heat reuse is supported but must not introduce operational dependency.

Sensitivity

Sites with guaranteed heat offtake may increase reuse integration.

4.6 Digital Twin Authority Model

Decision
Digital twin operates in bounded supervisory mode, without authority over safety interlocks.

Alternatives Considered

Full autonomous control
Monitoring-only model

Tradeoffs

Mode	Advantages	Disadvantages
Autonomous	Maximum automation potential	Increased safety and validation risk
Monitoring only	Maximum safety	Limited operational optimization
Supervisory bounded (selected)	Balanced safety and optimization	Requires defined authority boundaries

Rationale

The twin provides operational optimization while preserving deterministic safety behavior.

Safety-critical interlocks remain hardware- or PLC-enforced.

Sensitivity

Future validated models may expand operational authority.

4.7 Cooling Topology Independence from Hardware Vendors

Decision
Facility cooling architecture remains vendor-agnostic at the CDU boundary.

Alternatives Considered

Hardware-specific cooling integration

Tradeoffs

Approach	Advantages	Disadvantages
Vendor-specific	Maximum optimization for specific hardware	Reduces flexibility, increases lock-in
Vendor-agnostic (selected)	Maximum flexibility, supports hardware evolution	Requires interface abstraction

Rationale

Facility lifetime exceeds IT hardware lifetime.

Vendor-neutral interfaces preserve long-term adaptability.

4.8 Summary

The selected architecture represents a balanced operating point within the physically admissible region defined by Appendices A–F.

The chosen decisions prioritize:

Fault containment
Operational independence
Thermal and hydraulic efficiency
Commissionability
Long-term adaptability

These selections establish a reference architecture that is physically grounded, operationally robust, and adaptable to evolving AI workloads.

5. Sizing Envelopes (Outputs)

5.1 Thermal

Item	Value (initial)
Heat to liquid	9.5–10 MW
$\Delta T$ design	10 K
Estimated flow	derived in Appendix B
CDU capacity	N+1

5.2 Electrical

Item	Value
IT power	10 MW
Ancillary	~8–12%
Diversity	workload dependent

5.3 Water

Header sizing per hydraulic model
Treatment plant sized for volume turnover

5.4 Observability

1 s resolution for critical paths
10 s for secondary
Retention ≥ 24 months

6. Commissioning & Evidence Plan

For each contract:

Method
- FAT
- SAT
- IST
- HIL
Instrumentation
- Calibrated meters
- Flow/temperature pairs
- Power analyzers
Acceptance
- Numeric criteria
- Stability windows
- Negative tests
Artifacts
- Reports
- Traces
- As-built configs

7. Operational Model

Change governance
Maintenance schedules
Alarm philosophy
Training requirements
Failure drills

Document Status

Version: Draft 1.0
Nature: Engineering Basis of Design
Ownership: Multidisciplinary

Appendix Index (authoritative derivations and evidence mapping)

Appendix A — Workload → Boundary Projection
Appendix B — Thermal Physics and Digital Twin Basis
Appendix C — Hydraulics, Piping, and $\Delta P$ Budgets
Appendix D — Sustainability Model and KPI Closure
Appendix E — Cross-Domain FMEA and Commissioning Mapping
Appendix F — CausalCompute Alignment (Witness Workload Closure)

Appendix A — Workload → Boundary Projection

A.1 Purpose

This appendix translates arbitrary AI training objectives into the electrical and thermal quantities visible at the facility boundary.

The facility is intentionally workload-agnostic.
Therefore the mathematics is used to generate:

admissibility envelopes, not a single model instance
power transients, not GPU counts
boundary quantities ($P_{IT}$, $\Delta P$, $dP/dt$)

A.2 Notation

Symbol	Meaning	Units
$P$	model parameters	params
$Tok$	total training tokens	tokens
$T$	wall-clock budget	s
$c$	FLOPs per param-token (dense ≈ 6)	FLOPs/(param·token)
$\eta$	sustained training efficiency	–
$\varepsilon_{comp}$	compute efficiency at IT boundary	FLOPs/s/W
$P_{IT}$	IT electrical power	W
$\Delta P$	step change in power	W
$dP/dt$	ramp rate	W/s

A.3 Compute Demand

Total algorithmic work:

$$ F_{total} = c \cdot P \cdot Tok $$

Required sustained throughput:

$$ F_{req} = \frac{F_{total}}{T} $$

Mapping to electrical boundary:

$$ P_{IT,derived} = \frac{F_{req}}{\eta \cdot \varepsilon_{comp}} $$

Admissibility condition

$$ P_{IT,derived} \le P_{IT,envelope} $$

For this pod:

$$ P_{IT,envelope} = 10\ \text{MW} $$

This relation does not size the facility to one model;
it checks whether any proposed workload lies inside the envelope.

A.4 Transient Abstraction

AI training creates power transients through:

job start/stop
collective synchronizations
checkpoint I/O
failure recovery

Detailed behavior is reduced to enforceable limits:

$$ |\Delta P| \le \Delta P_{max} $$

$$ \left|\frac{dP}{dt}\right| \le (dP/dt)_{max} $$

PoC Envelope (per 2 MW block)

$$ \Delta P_{block} \le 0.2\ \text{MW in 1 s} $$

$$ \left|\frac{dP_{block}}{dt}\right| \le 0.1\ \text{MW/s} $$

Recovery objective:

$$ t_{rec,block} \le 10\text{–}30\ \text{s} $$

Per Rack (100 kW baseline)

$$ \Delta P_{rack} \le 10\ \text{kW in 1 s} $$

$$ \left|\frac{dP_{rack}}{dt}\right| \le 5\ \text{kW/s} $$

A.5 Admissible Workload Set

The facility admits any workload whose boundary image lies in:

$$ \mathcal{A} = \left{ \begin{aligned} P(t) &\le 10\ \text{MW} \\ |\Delta P| &\le 0.2\ \text{MW/block} \\ |dP/dt| &\le 0.1\ \text{MW/s} \\ T_{TC} &\in [T_{min},T_{max}] \\ \dot m &\ge \dot m_{min} \end{aligned} \right. $$

Workload mathematics therefore act as the projection operator into this admissible set.

A.6 Conceptual Shift

Locked design

$$ (P, Tok, T) \rightarrow \text{exact GPU count} \rightarrow \text{facility} $$

Agnostic design

$$ (P, Tok, T) \rightarrow (P_{IT},\ \Delta P,\ dP/dt) \rightarrow \text{facility envelopes} $$

A.7 Scheduler ↔ Facility Interface

Enforcement Layers

Primary – Scheduler Policy
- staged energization
- anti-herd starts
- block-local ramp sequencing
Secondary – Power Capping
- per-rack limits
- collective smoothing
Tertiary – BESS/UPS
- grid event absorption
- residual transient buffer

A.8 Verification Method

Acceptance requires replay of representative traces:

voltage sag within limits
UPS not overloaded
CDU controls stable
$T_{out}$ within envelope

A.9 Definition

In the agnostic formulation, workload mathematics serve to map arbitrary ML objectives into boundary quantities rather than prescribe a specific model instance.

A.10 Outputs to Facility Design

This appendix produces:

IT power envelope ($P_{IT}$)
transient limits ($\Delta P$, $dP/dt$)
inputs to thermal sizing (Appendix B)
acceptance tests for commissioning

A.11 Witness Reference

A single worked witness is maintained in Appendix F (CausalCompute alignment).
All numeric witness values used by Appendices B–E are sourced from Appendix F.

End of Appendix A

Appendix B — Thermal Physics and Digital Twin Basis (with Full Derivations)

B.1 Purpose

This appendix closes the thermodynamic and control loop for the single witness workload defined in Appendix F:

$P_{IT} \approx 4.77\ \text{MW}$
$\dot Q \approx P_{IT}$ (all IT power becomes heat, first order)
Design liquid rise: $\Delta T = 12^\circ\text{C}$ (envelope 8–15 °C)
Mechanical zoning: $1\ \text{MW}$ maximum fault domain per zone

It produces:

Required coolant flow $\dot m,\ \dot V$ at the pod boundary
Per-zone flow targets
Pumping power order-of-magnitude from $\Delta P$ budgets
A control-oriented thermal state model and time constants
Commissioning identification and validation gates for the twin

B.2 Notation and Constants

Symbol	Meaning	Units
$\dot Q$	heat rate	W
$P_{IT}$	IT electrical power	W
$\dot m$	mass flow rate	kg/s
$\dot V$	volumetric flow rate	m$^3$/s
$\rho$	fluid density (water, 25–30 °C)	kg/m$^3$
$c_p$	specific heat (water)	J/(kg·K)
$\Delta T$	temperature rise	K or °C
$\Delta P$	pressure differential	Pa
$\eta_{pump}$	pump + motor + VFD efficiency	–
$C$	effective thermal capacitance	J/K
$\tau$	thermal time constant	s

Water properties (PoC design basis)

$\rho \approx 997\ \text{kg/m}^3$
$c_p \approx 4180\ \text{J/(kg·K)}$

B.3 Thermodynamic Closure (Heat → Flow)

B.3.1 Fundamental single-phase relation

For an incompressible single-phase coolant loop:

$$ \dot Q = \dot m, c_p, \Delta T $$

Rearranging gives required mass flow:

$$ \dot m = \frac{\dot Q}{c_p,\Delta T} $$

Using density to convert to volumetric flow:

$$ \dot V = \frac{\dot m}{\rho} $$

B.3.2 Witness workload heat rate

$$ \dot Q \approx P_{IT} \approx 4.77\times10^6\ \text{W} $$

B.3.3 Pod-level mass flow

With $\Delta T = 12^\circ\text{C}$:

$$ \dot m = \frac{4.77\times10^6}{4180 \times 12} $$

Compute denominator:

$$ 4180\times 12 = 50{,}160 $$

So:

$$ \dot m \approx \frac{4.77\times10^6}{50{,}160} \approx 95.1\ \text{kg/s} $$

B.3.4 Pod-level volumetric flow

$$ \dot V = \frac{95.1}{997} \approx 0.0954\ \text{m}^3/\text{s} \approx 95\ \text{L/s} $$

Pod-level result (witness case)

$$ \boxed{\dot m \approx 95.1\ \text{kg/s}},\qquad \boxed{\dot V \approx 0.095\ \text{m}^3/\text{s}\approx 95\ \text{L/s}} $$

B.4 Zone-Level Distribution (1 MW Fault Domains)

B.4.1 Per-zone flow at 1 MW

For a zone cap of $\dot Q_{zone} = 1\ \text{MW}$:

$$ \dot m_{zone} = \frac{1.0\times10^6}{4180 \times 12} \approx 19.9\ \text{kg/s} $$

$$ \dot V_{zone} = \frac{19.9}{997} \approx 0.0200\ \text{m}^3/\text{s} \approx 20.0\ \text{L/s} $$

Per-zone result

$$ \boxed{\dot V_{zone} \approx 20\ \text{L/s}\ \text{per}\ 1\ \text{MW zone at}\ \Delta T=12^\circ\text{C}} $$

B.4.2 Mapping the witness workload to zones

Witness load is served by approximately five 1 MW zones in aggregate:

$$ \frac{4.77\ \text{MW}}{1\ \text{MW/zone}} \approx 4.77\ \text{zones} $$

Nominal flow if distributed across 5 zones:

$$ 5 \times 20\ \text{L/s} = 100\ \text{L/s} $$

This matches the pod-level 95 L/s within rounding and distribution overheads.

B.5 Rack-Level Sanity (100 kW Baseline)

For a 100 kW rack:

$$ \dot m_{rack} = \frac{100{,}000}{4180\times 12} \approx 1.99\ \text{kg/s} $$

$$ \dot V_{rack} \approx \frac{1.99}{997} \approx 0.0020\ \text{m}^3/\text{s} \approx 2.0\ \text{L/s} $$

B.6 Pumping Power ($\Delta P$ Budget → Watts)

$$ P_{pump} \approx \frac{\Delta P \cdot \dot V}{\eta_{pump}} $$

B.6.1 Zone pumping order-of-magnitude

Assume a PoC zone budget:

$\Delta P_{zone} = 100\ \text{kPa} = 100{,}000\ \text{Pa}$
$\dot V_{zone} \approx 0.020\ \text{m}^3/\text{s}$
$\eta_{pump} = 0.70$

$$ P_{pump,zone} \approx \frac{100{,}000 \times 0.020}{0.70} \approx 2{,}857\ \text{W} \approx 2.9\ \text{kW} $$

If the witness workload uses ~5 zones:

$$ P_{pump,total} \approx 5 \times 2.9\ \text{kW} \approx 14.5\ \text{kW} $$

B.7 Thermal State Model (Digital Twin Anchor)

B.7.1 First-order energy balance

$$ C\frac{dT_{out}}{dt} = \dot Q(t) - \dot m(t),c_p,\big(T_{out}(t) - T_{in}(t)\big) $$

This is a control-oriented abstraction sufficient for estimation, anomaly detection, and supervisory setpoint control.

B.7.2 Steady-state check

At steady state:

$$ \dot Q \approx \dot m c_p (T_{out}-T_{in}) \Rightarrow \Delta T \approx \frac{\dot Q}{\dot m c_p} $$

B.8 Time Constant and Transient Behavior

Dominant time constant:

$$ \tau = \frac{C}{\dot m c_p} $$

Illustrative inventory:

$V_{eq} \approx 5\ \text{m}^3$
$m_{eq} \approx 5000\ \text{kg}$

$$ C \approx m_{eq} c_p \approx 5000 \times 4180 \approx 2.09\times 10^7\ \text{J/K} $$

With $\dot m \approx 20\ \text{kg/s}$:

$$ \dot m c_p \approx 20\times 4180 = 83{,}600\ \text{W/K} $$

$$ \tau \approx \frac{2.09\times10^7}{83{,}600} \approx 250\ \text{s} $$

B.9 Discrete-Time Estimator (Online Digital Twin)

For sampling interval $\Delta t$:

$$ \hat T_{out}[k+1] = \hat T_{out}[k] + \frac{\Delta t}{\hat C} \left( \dot Q[k]

\dot m[k],c_p,(\hat T_{out}[k]-T_{in}[k]) \right) $$

Telemetry sources:

$\dot Q[k]$: rack/block power metering
$\dot m[k]$: flow meter
$T_{in}[k]$: supply temperature
$T_{out}[k]$: return temperature probe

B.10 Commissioning Identification of $C$ (Evidence Gate)

Procedure:

Hold $T_{in}$ approximately constant
Hold $\dot m$ constant
Apply a bounded step or ramp in $\dot Q$
Measure $T_{out}(t)$
Fit $\hat C$ by minimizing prediction error

Acceptance (PoC intent):

$$ \text{RMSE}(T_{out}) \le 0.5^\circ\text{C} $$

B.12 Outputs Exported (Witness Case)

Pod-level flow: $$ \dot V \approx 0.095\ \text{m}^3/\text{s} \approx 95\ \text{L/s} $$
Zone-level flow: $$ \dot V_{zone} \approx 0.020\ \text{m}^3/\text{s} \approx 20\ \text{L/s} $$
Rack flow: $$ \dot V_{rack} \approx 2\ \text{L/s} $$
Zone time constant (illustrative): $$ \tau \approx 250\ \text{s} $$

Appendix C — Hydraulics, Piping, and $\Delta P$ Budgets

C.1 Purpose

This appendix converts the thermal requirements from Appendix B into buildable hydraulic quantities:

header diameters from the single witness flow ($\approx 95\ \text{L/s}$)
per-zone distribution at $\approx 20\ \text{L/s}$
velocity and $\Delta P$ budgets
pumping power and sensitivity
fault-domain containment rules

All calculations are SI; water at 25–30 °C is assumed.

C.2 Continuity → Pipe Diameter

For design velocity $v$:

$$ A = \frac{\dot V}{v}, \qquad d = \sqrt{\frac{4A}{\pi}} $$

C.2.2 Pod-level header (witness case)

From Appendix B:

$$ \dot V \approx 0.095\ \text{m}^3/\text{s}\ (95\ \text{L/s}) $$

Use $v = 2.0\ \text{m/s}$:

$$ A = \frac{0.095}{2.0} = 0.0475\ \text{m}^2 $$

$$ d = \sqrt{\frac{4 \times 0.0475}{\pi}} \approx 0.246\ \text{m} $$

$$ \boxed{d \approx 0.25\ \text{m}} $$

Interpretation

Primary header class ≈ DN250 (DN250–DN300 depending on allowances)
The full 10 MW pod (200 L/s) would approach DN350 class

C.3 Zone Branch Sizing

Zone flow:

$$ \dot V_{zone} \approx 0.020\ \text{m}^3/\text{s}\ (20\ \text{L/s}) $$

Using $v=2.0\ \text{m/s}$:

$$ A_{zone} = \frac{0.020}{2.0} = 0.010\ \text{m}^2 $$

$$ d_{zone} = \sqrt{\frac{4\times0.010}{\pi}} \approx 0.113\ \text{m} $$

$$ \boxed{d_{zone} \approx 110\ \text{mm}} $$

Practical class: DN100–DN125 per 1 MW zone.

C.4 Rack Manifold Sanity

For 100 kW rack:

$$ \dot V_{rack} \approx 2\ \text{L/s} = 0.002\ \text{m}^3/\text{s} $$

If internal manifold velocity target $v=1.5\ \text{m/s}$:

$$ A_{rack} = \frac{0.002}{1.5} = 0.00133\ \text{m}^2 $$

$$ d_{rack} \approx 0.041\ \text{m} $$

Approx: DN40 class at rack interface.

C.5 $\Delta P$ Budget Philosophy

$$ P_{pump} = \frac{\Delta P \cdot \dot V}{\eta} $$

C.5.1 PoC zone budget

Segment	Target $\Delta P$
Rack cold plates & hoses	≤ 40 kPa
CDU HEX + internals	≤ 40 kPa
Distribution & valves	≤ 20 kPa
Total zone	≤ 100 kPa

C.5.2 Zone pumping power (order-of-magnitude)

$$ \dot V_{zone} = 0.020\ \text{m}^3/\text{s},\quad \Delta P = 100{,}000\ \text{Pa},\quad \eta = 0.70 $$

$$ P_{pump,zone} = \frac{100{,}000 \times 0.020}{0.70} \approx 2.9\ \text{kW} $$

Sensitivity:

$$ P_{pump} \propto \Delta P $$

C.6 Velocity Limits (Rationale)

Location	Limit	Reason
Primary headers	≤ 2.0 m/s	erosion, noise, transients
Secondary runs	≤ 1.5 m/s	controllability
Rack hoses	≤ 1.2 m/s	connector wear
Drain lines	≥ 0.6 m/s	sediment transport

C.7 Transient & Water Hammer Considerations

Rapid valve closure can generate:

$$ \Delta P_{wh} \approx \rho a \Delta v $$

Mitigations:

rate-limited actuators
surge arrestors
controlled pump ramps
commissioning verification of worst-case closures

C.8 Segmentation and Fault Domains

Containment rule:

A single failure shall not exceed 1 MW thermal radius.

Therefore:

isolation valves at each zone boundary
no common headers without sectionalization
wet components segregated from electrical rooms

Design spill volume per zone:

$$ V_{spill,max} = \dot V_{zone} \times t_{detect} $$

With 20 L/s and 10 s detection:

$$ V_{spill,max} \approx 200\ \text{L} $$

C.9 Instrumentation Requirements

Minimum per zone:

supply $T_{TC,in}$
return $T_{TC,out}$
flow $\dot m$ or $\Delta P$ proxy
valve position
leak detection (cable + point)

C.10 Commissioning Evidence

Acceptance tests derived from this appendix:

Flow verification: $$ \dot V_{zone} \ge 20\ \text{L/s} $$
$\Delta P$ envelope: $$ \Delta P_{zone} \le 100\ \text{kPa} $$
Velocity audit: confirm $v \le 2\ \text{m/s}$ in primaries
Transient test: staged valve closure without excursions
Leak isolation: single-zone containment proven

Appendix D — Sustainability Model and KPI Closure (Witness-Case Extended)

D.1 Purpose

This appendix converts the single witness workload into auditable sustainability quantities:

annual energy (IT and facility)
heat export potential ($\text{MWh}_{th}$)
water sensitivity under adiabatic/evaporative augmentation
KPI boundaries and required metering
a PoC measurement plan that makes reporting defensible

The intent is not “green claims,” but metered contracts.

D.2 Inputs from the Witness Case

From Appendix F:

$$ P_{IT} \approx 4.77\ \text{MW} $$

Design intent:

$\text{PUE}_{design} = 1.15$
utilization factor $U = 0.70$ (example)

Facility power:

$$ P_{fac} = P_{IT} \times \text{PUE} $$

$$ P_{fac} \approx 4.77 \times 1.15 = 5.4855\ \text{MW} $$

D.3 Annual Energy ($\text{MWh/year}$)

D.3.1 IT energy

$$ E_{IT,year} = P_{IT} \times 8760 \times U $$

Compute:

$$ E_{IT,year} \approx 4.77 \times 8760 \times 0.70 \approx 29{,}300\ \text{MWh/yr} $$

D.3.2 Facility energy

$$ E_{fac,year} = P_{fac} \times 8760 \times U $$

$$ E_{fac,year} \approx 5.4855 \times 8760 \times 0.70 \approx 33{,}600\ \text{MWh/yr} $$

D.3.3 Overhead energy (derived)

$$ E_{overhead,year} = E_{fac,year} - E_{IT,year} \approx 4{,}300\ \text{MWh/yr} $$

D.4 Heat Reuse Potential

Thermal energy available at IT boundary (first order):

$$ \dot Q \approx P_{IT} $$

Annual thermal energy:

$$ E_{heat,year} \approx P_{IT} \times 8760 \times U \approx 29{,}300\ \text{MWh}_{th}\text{/yr} $$

Heat pump relation (if needed):

If $COP = \frac{Q_{delivered}}{W_{hp}}$:

$$ W_{hp} = \frac{Q_{delivered}}{COP}, \qquad Q_{source} = Q_{delivered}\left(1-\frac{1}{COP}\right) $$

D.5 Water Sensitivity (Adiabatic/Evaporative Augmentation)

Latent heat of vaporization:

$$ h_{fg} \approx 2.45\ \text{MJ/kg} $$

Evaporation mass flow to reject heat $Q$:

$$ \dot m_{evap} \approx \frac{Q}{h_{fg}} $$

For $Q = 4.77\ \text{MW} = 4.77\ \text{MJ/s}$:

$$ \dot m_{evap} \approx \frac{4.77}{2.45}\ \text{kg/s} \approx 1.95\ \text{kg/s} \approx 1.95\ \text{L/s} $$

Daily water (if operating adiabatic continuously):

$$ V_{day} \approx 1.95\ \text{L/s} \times 86400\ \text{s/day} \approx 168{,}000\ \text{L/day} \approx 168\ \text{m}^3/\text{day} $$

Annual at utilization $U=0.70$:

$$ V_{year} \approx 168\ \text{m}^3/\text{day}\times 365 \times 0.70 \approx 43{,}000\ \text{m}^3/\text{yr} $$

D.6 KPI Definitions (Time-Series, Not Scalars)

D.6.1 $\text{PUE}(t)$

$$ \text{PUE}(t) = \frac{P_{fac}(t)}{P_{IT}(t)} $$

Requirements:

computed as a time series with time-aligned meters
reported as distributions/percentiles, not a single number

D.6.2 $\text{WUE}(t)$

Where make-up water exists:

$$ \text{WUE}(t) = \frac{\dot V_{makeup}(t)}{P_{IT}(t)} $$

Interval form:

$$ \text{WUE}_{interval} = \frac{V_{makeup}}{E_{IT}}\quad [\text{L/kWh}] $$

D.6.3 Heat export metering

Exported thermal power:

$$ \dot Q_{export}(t) = \rho,c_p,\dot V_{export}(t),\Delta T_{export}(t) $$

Exported energy:

$$ E_{export} = \int \dot Q_{export}(t),dt $$

D.6.4 Carbon (operational)

If grid intensity is a time series $I_{grid}(t)$ in kgCO$_2$e/kWh:

$$ CO2e = \int I_{grid}(t),P_{fac}(t),dt $$

D.7 Metering Contract (Minimum Required Meters)

Electrical:

Utility import meter (true RMS, time-stamped)
Plant distribution meters (cooling, UPS losses, BESS auxiliaries)
IT boundary meters per block / PDU / RPP (depending on design)

Thermal / Water:

Heat meter at export interface: $\dot V + T_{supply} + T_{return}$
FW/TC loop meters per zone: $\dot V$, $T_{in}$, $T_{out}$, $\Delta P$
Make-up water meter where adiabatic exists

Time synchronization:

PTP/NTP such that meter timestamps are aligned and drift is monitored

D.8 “Fails to Ambient” Export Philosophy (Reliability Constraint)

Heat export must not become a single point of failure.

Contractual rule:

Export path must fail open to ambient rejection.
Off-taker unavailability shall not cause derate of IT load.

This implies bypass and buffering at the export interface.

D.9 Witness-Case Sustainability Summary

Using $P_{IT}=4.77\ \text{MW}$, $U=0.70$, $\text{PUE}=1.15$:

Quantity	Result
IT annual energy $E_{IT}$	~29,300 MWh/yr
Facility annual energy $E_{fac}$	~33,600 MWh/yr
Overhead energy	~4,300 MWh/yr
Heat potential $E_{heat}$	~29,300 $\text{MWh}_{th}$/yr
Evaporation rate (adiabatic continuous)	~1.95 L/s
Daily water (adiabatic continuous)	~168 $\text{m}^3$/day
Annual water (adiabatic continuous, $U=0.70$)	~43,000 $\text{m}^3$/yr

Interpretation: even at ~5 MW class loads, adiabatic hours must be explicitly controlled and metered.

D.10 PoC Verification Plan

To make the PoC defensible:

Verify $P_{IT}(t)$, $P_{fac}(t)$ and compute $\text{PUE}(t)$
Verify heat balance closure: $$ P_{IT} \approx \rho c_p \dot V \Delta T + \text{loss terms} $$
If export exists, verify heat meter accuracy and availability
If adiabatic exists, verify make-up meter and compute $\text{WUE}(t)$
Time-sync audit: confirm timestamp alignment across power + flow + temperature

Acceptance intent: all reported KPIs must be reproducible from raw time-series data with documented calibrations.

Appendix E — Cross-Domain FMEA and Commissioning Mapping (Witness-Case)

E.1 Purpose

This appendix applies a structured Failure Modes and Effects Analysis (FMEA) to the
10 MW PoC architecture while explicitly referencing the single witness workload (Appendix F):

$P_{IT} \approx 4.77\ \text{MW}$
$\dot V \approx 95\ \text{L/s}$
$\dot V_{zone} \approx 20\ \text{L/s}$
$\tau \approx 250\ \text{s}$ (illustrative)

The objective is to:

Identify failure modes that could violate the envelopes derived in Appendices A–D
Quantify risk using the common O/S/D scale
Map each high-RPN item to a commissioning evidence gate

E.2 Scoring Method (recap)

Risk Priority Number:

$$ RPN = O \times S \times D $$

Range	Action
≥300	Architectural redesign
200–299	Mandatory mitigation + tests
120–199	Mitigation required
60–119	Manage with monitoring
<60	Accept / monitor

E.3 Electrical Domain (Witness-Linked)

Failure Mode	O	S	D	RPN	Witness Impact	Mitigation	Commissioning Evidence
Block ramp exceeds envelope	5	8	4	160	Violates $dP/dt$ limits	Scheduler staging + capping	HIL replay of ramps
Protection mis-coordination	3	9	6	162	Upstream trip near block limits	Settings governance	Selectivity test
UPS bypass failure	2	9	6	108	Loss of power quality	Periodic transfer tests	Bypass SAT
Harmonics at PCC	4	5	5	100	PQ breach	Filters + monitoring	PQ report
Powered but uncooled	3	10	6	180	Thermal runaway	Hard interlocks	Interlock FAT

E.4 Mechanical Domain

Failure Mode	O	S	D	RPN	Witness Link	Mitigation	Evidence
Loss of flow in 1 MW zone	4	9	5	180	$20\ \text{L/s}$ drop	Dual CDU + alarms	Flow fail test
Valve hunting	5	6	6	180	Violates $\tau$ model	Rate limits	Step response
Filter fouling	6	5	4	120	$\Delta P > 100\ \text{kPa}$	DP trending	PM records
Leak at rack	4	8	4	128	~200 L spill	Trays + isolation	Leak drill
Air ingress	4	7	6	168	Oscillatory $\Delta P$	Degassing	Stability test

E.5 Digital Twin & Controls

Failure Mode	O	S	D	RPN	Witness Link	Mitigation	Evidence
Sensor drift	6	7	6	252	Bias in $T_{out}$	Redundancy	Calibration
Model obsolete	5	7	7	245	Wrong $\tau$	BIM versioning	Re-fit gate
Time sync loss	5	6	7	210	KPI corruption	PTP/NTP	Audit
Unsafe actuation	3	10	6	180	Flow violation	Guardrails	Negative test

E.6 Sustainability Risks

Failure Mode	O	S	D	RPN	Witness Link	Mitigation	Evidence
Unmetered PUE	6	6	7	252	KPI invalid	Meter plan	Data audit
Stranded heat	6	6	6	216	Export not utilized	Fail-open	Contract
Water cap breach	4	8	6	192	Adiabatic overuse	Dry baseline	WUE logs

E.7 Commissioning Matrix

E.7.1 Electrical Tests

Replay ramp to confirm: $$ \left|\frac{dP}{dt}\right| \le 0.1\ \text{MW/s} $$
Verify per-block metering and coordination
Bypass and transfer tests

E.7.2 Mechanical Tests

Prove: $$ \dot V_{zone} \ge 20\ \text{L/s} $$
Confirm: $$ \Delta P_{zone} \le 100\ \text{kPa} $$
Leak isolation within single zone

E.7.3 Twin Validation

RMSE: $$ \le 0.5^\circ\text{C} $$
Fault injection for drift and flow loss

E.7.4 Sustainability

Reproduce $\text{PUE}(t)$ from raw meters
Verify heat meter closure

E.8 Top Residual Risks

Sensor integrity for twin ($RPN=252$)
KPI auditability ($RPN=252$)
Model validity after changes ($RPN=245$)

Mitigation requires process + engineering, not hardware alone.

E.9 Conclusion

The witness workload demonstrates:

envelopes can be met
failure modes are observable
each risk maps to a testable gate

No $RPN \ge 300$ remains after mitigations.

Appendix F — CausalCompute Alignment (Witness Workload Closure)

F.1 Purpose

This appendix demonstrates that the envelopes defined in the Basis of Design can host a representative AI training workload using an external first-principles sizing engine (CausalCompute, Steps 0–2).

This appendix is:

a traceability bridge between ML intent and facility physics,
an evidence layer showing that the BoD envelopes are internally consistent,
a generator of measurable PoC acceptance criteria.

This appendix is not:

a redesign of the facility,
a procurement specification,
a network topology design,
a replacement for the thermo-hydraulic derivations in Appendices A–C.

F.2 Lifecycle Status

F.2.1 Status of the Basis of Design

The BoD is a pre-production engineering contract, not an as-built system.
It defines envelopes and evidence gates that detailed design must later satisfy.

F.2.2 Status of CausalCompute

CausalCompute is used here as a PoC witness engine.

Allowed conclusions:

envelope admissibility at the facility boundary (MW, L/s, kW/rack)
sensitivity to explicit assumptions ($\eta$, $\Delta T$, checkpoint policy)

Disallowed conclusions:

procurement GPU counts or guarantees
network topology or congestion claims
ramp compliance verification
reliability closure (N+1) or operational readiness

F.3 Methodological Duality — Bottom-Up vs Top-Down

BoD — Bottom-Up (Facility-First)
Power → Heat → Fluid → Space → Operations
		 |________________________________
										  |
Workload → FLOPs → Time → GPUs → Power → Heat
CausalCompute — Top-Down (Workload-First)

Convergence: heat is the handoff point.

The tool delivers an implied heat rate:

$$ \dot Q_{\text{tool}} \approx P_{IT} $$

The BoD accepts or rejects that heat rate using its $\Delta T$, flow, zoning, and rejection limits.

F.4 Scope and Cross-References

Domain	Primary Reference
Workload → boundary mapping	Appendix A
Thermal closure	Appendix B
Hydraulics & $\Delta P$	Appendix C
Sustainability accounting	Appendix D
FMEA & commissioning	Appendix E

F.5 Inputs to the Witness Calculation

F.5.1 Workload

Item	Value
Parameters	$4.05\times10^{11}$
Tokens	$3\times10^{12}$
Deadline	60 days
FLOPs/param-token	6

F.5.2 Platform Abstractions

Item	Value
Device sustained	0.875 PFLOP/s
Device memory	80 GB
$\eta_{\text{compute}}$	0.30
$\eta_{\text{fabric}}$	0.80

F.5.3 Facility Envelopes (BoD)

Envelope	Value
IT power	≤ 10 MW
$\Delta T$ liquid	12 °C (8–15)
Rack cap	100 kW
Zone cap	1 MW
Flow rule	~20 L/s per MW

F.6 Step-0 — Topology-Agnostic Invariants

Quantity	Result
Required throughput	1.41 EFLOP/s
Token rate	$5.79\times10^5$ tok/s
Checkpoint size	810 GB
Max step time	69 s

F.7 Step-1 — Minimal Feasible Cluster (Witness)

Item	Result
GPUs	6,208
Nodes	776 (8 GPU/node)
Parallelism	DP/TP/PP = 97/16/4
Step time	68.9 s ≤ 69 s
Memory/device	52 GB ≤ 80 GB

F.8 Step-2 → BoD Boundary Projection

F.8.1 Power Alignment

Quantity	Result	Envelope	Status
IT power	4.77 MW	≤ 10 MW	Aligned
Facility power	5.49 MW	—	—
PUE	1.15	BoD target	aligned

F.8.2 Thermal Alignment

Quantity	Result (SI)	Practical Equivalent	Rule	Status
Heat	4.77 MW	—	9.5–10 MW cap	Aligned
Coolant flow	0.095 m$^3$/s	95 L/s (5,700 L/min)	20 L/s per MW	Aligned
Per-zone load	~0.95 MW	—	≤ 1 MW	Aligned

Using Appendix B:

$$ \dot m = \frac{\dot Q}{c_p , \Delta T} $$

F.8.3 Rack Density

Item	Result (SI)	Practical Equivalent	Limit	Status
Racks	49	—	—	—
IT per rack	97 kW	(≈ 331,000 BTU/h)	100 kW	Aligned

F.8.4 Hydraulics

Flow per zone ≈ 20 L/s (≈ 1,200 L/min)
Header class consistent with DN200–DN250
Pumping power remains kW-scale

F.9 Alignment Statement

The witness workload lies inside all BoD envelopes for electrical, thermal, hydraulic, and rack constraints.

F.10 Sensitivities

Change	Effect
$\eta_{\text{compute}}\downarrow$	GPUs ↑ → IT power ↑
$\Delta T\downarrow$ to 8 K	Flow ↑ ~50%
Shorter checkpoint	Storage BW ↑
$\eta_{\text{fabric}}\downarrow$	Step time ↑ → GPUs ↑

F.11 PoC Evidence Gates

Power → heat closure: $$ \dot Q \approx P_{IT} $$
Flow law: $$ \dot m = \frac{\dot Q}{c_p , \Delta T} $$
Ramp compliance: per Appendix A
Digital twin accuracy: per Appendix B

End of Appendix F

Design Brief — Reference Architecture (PoC)

This document instantiates the Engineering Basis of Design (BoD) into a coherent 10 MW reference topology.

This document contains no original requirements and no original derivations.
Requirements are defined in sections above.

Executive Summary

This document defines a 10 MW AI-native data-center pod derived from physics rather than historical templates:

Workload → FLOP → Watts → Heat → Water → Space → Operations

Key principles:

Bounded fault domains — 2 MW electrical blocks aligned to 1 MW mechanical zones prevent local failures from becoming site events.
Explicit transients — sized against verified ramp envelopes ($\Delta P$, $dP/dt$), not steady-state MW alone. (See Appendix A.)
Closed-loop operations — a physics-based digital twin supervises within hard interlocks and auditable safety limits. (See Appendix B.)

The architecture is intentionally vendor-neutral and deployable across European jurisdictions.

1. Why This Is Needed

AI workloads have broken classical datacenter assumptions:

Power density: 5–15 kW/rack → 30–150+ kW/rack
Heat path: air → liquid-dominated
Utilization: workload-bound, not facility-bound
Deadlines: training schedules compete with time-to-power

Therefore infrastructure must be derived from workload physics, not legacy layouts.

2. Boundary Conditions

Fixed by Reality

Grid capacity and ramp constraints
European limits on water, noise, and heat rejection
Reliability targets (N+1 / optional 2N)
Mixed customer hardware maintainability

Design Freedoms

Cooling topology (D2C/RDHx/hybrids)
Electrical architecture (UPS/BESS placement)
Spatial modularization
Digital-twin control strategy

3. Inputs from the AI Domain

Model size, tokens, deadline
Implied sustained FLOP/s
Availability & jitter tolerance
Hardware class envelope (TDP, $\Delta T$ limits)

Workload-to-boundary mapping is defined in Appendix A.
Witness closure via CausalCompute is defined in Appendix F.

4. Reference Topology (Instantiation)

IT Load: 10 MW envelope (BoD)
Rack baseline: 100 kW class
Cooling: warm-water D2C with CDU layer
Electrical blocks: 2 MW fault/coordination domains
Mechanical zones: 1 MW maximum fault domains

Derived flow rules, $\Delta T$ envelopes, header classes, and $\Delta P$ budgets are defined in Appendices B and C.

5. Electrical Architecture (Instantiation)

Utility → MV → LV distribution aligned to 2 MW blocks
Per-block metering at the IT boundary (BoD observability contract)
Selective coordination implemented per BoD electrical contract
Interlock: rack enable requires cooling availability (BoD thermal contract)

Transient contract is defined in Appendix A and verified per Appendix E.

6. Mechanical Architecture (Instantiation)

FW loop to dry coolers (baseline)
CDU layer separating FW/TC
Zone isolation at 1 MW boundaries
Residual air path for ancillaries

Thermal closure and twin model basis are defined in Appendix B.
Hydraulics, pipe classes, and $\Delta P$ budgets are defined in Appendix C.

7. Sustainability Architecture (Instantiation)

Metering topology and KPI computation per Appendix D
Export interface is fail-open to ambient rejection per Appendix D
KPI reporting is time-series, not scalar summaries

8. Digital Twin Concept (Instantiation)

The twin uses the first-order energy balance defined in Appendix B, operating in modes:

Observe → Recommend → Bounded Actuate.

Authority boundaries: cannot override hard interlocks (BoD safety/thermal contracts).

9. Commissioning Philosophy (Instantiation)

Progressive energization
Negative testing
Twin validation before authority
Evidence-based acceptance

Test matrix and FMEA mapping are defined in Appendix E.

10. Deliverables to Detailed Design

Electrical studies (load-flow, protection, harmonics)
Hydraulic model and transient analysis
Controls I/O and interlock matrix
Twin data schema
BIM constraints

Core Principle

Infrastructure decisions are derivations from physics and workload, not brand templates.

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Authority Model

Engineering Basis of Design

0. Executive Snapshot

1. Scope, Audience, Definitions

1.1 Audience

1.2 Boundary Definitions

1.3 Terminology

2. Architecture Contracts (Normative Core)

A. Electrical Contract

B. Thermal Contract

C. Water Contract

D. Observability Contract

E. Sustainability Contract

3. Reference Architecture Overview (Non-Normative Orientation)

3.1 Electrical

3.2 Mechanical

3.3 Controls

3.4 Safety

4. Architecture Tradeoffs and Design Decisions

4.1 Cooling Topology Selection

4.2 Thermal Rise ($\Delta T$) Selection

4.3 Mechanical Fault Domain Size

4.4 Electrical Fault Domain Size

4.5 Heat Rejection Strategy

4.6 Digital Twin Authority Model

4.7 Cooling Topology Independence from Hardware Vendors

4.8 Summary

5. Sizing Envelopes (Outputs)

5.1 Thermal

5.2 Electrical

5.3 Water

5.4 Observability

6. Commissioning & Evidence Plan

7. Operational Model

Document Status

Appendix A — Workload → Boundary Projection

A.1 Purpose

A.2 Notation

A.3 Compute Demand

A.4 Transient Abstraction

PoC Envelope (per 2 MW block)

Per Rack (100 kW baseline)

A.5 Admissible Workload Set

A.6 Conceptual Shift

A.7 Scheduler ↔ Facility Interface

Enforcement Layers

A.8 Verification Method

A.9 Definition

A.10 Outputs to Facility Design

A.11 Witness Reference

Appendix B — Thermal Physics and Digital Twin Basis (with Full Derivations)

B.1 Purpose

B.2 Notation and Constants

B.3 Thermodynamic Closure (Heat → Flow)

B.3.1 Fundamental single-phase relation

B.3.2 Witness workload heat rate

B.3.3 Pod-level mass flow

B.3.4 Pod-level volumetric flow

B.4 Zone-Level Distribution (1 MW Fault Domains)

B.4.1 Per-zone flow at 1 MW

B.4.2 Mapping the witness workload to zones

B.5 Rack-Level Sanity (100 kW Baseline)

B.6 Pumping Power ($\Delta P$ Budget → Watts)

B.6.1 Zone pumping order-of-magnitude

B.7 Thermal State Model (Digital Twin Anchor)

B.7.1 First-order energy balance

B.7.2 Steady-state check

B.8 Time Constant and Transient Behavior

B.9 Discrete-Time Estimator (Online Digital Twin)

$$ \hat T_{out}[k+1] = \hat T_{out}[k] + \frac{\Delta t}{\hat C} \left( \dot Q[k]

B.10 Commissioning Identification of $C$ (Evidence Gate)

B.12 Outputs Exported (Witness Case)

Appendix C — Hydraulics, Piping, and $\Delta P$ Budgets

C.1 Purpose