How accurate is a CDU capacity test? A measurement uncertainty worksheet

How accurate is a CDU capacity test?

The measured quantity is steady-state mean thermal power across named secondary CDU connections during the accepted interval. Gross exchanger transfer and net rack heat removal require different boundaries when pumps, bypasses or pipe heat exchange lie between them.

NIST Technical Note 1297, 1994 edition, distinguishes statistically evaluated Type A uncertainty from Type B uncertainty evaluated using other information, such as calibration certificates and specifications [S2]. Type A and Type B identify evaluation methods, not random versus systematic errors. An indication error is the indicated-minus-reference difference; a correction compensates for that error. Repeatability describes observed scatter, resolution describes the smallest reported increment, and uncertainty describes the remaining dispersion assigned to the result.

Use this worksheet for steady, single-phase liquid-to-liquid CDU tests. Liquid-to-air units require a heat-rejection boundary suited to their air side; two-phase operation requires an enthalpy model. The CDU commissioning procedure covers the mechanical and control sequence that makes the unit ready for this measurement.

Which conditions make a capacity rating comparable?

Compare kilowatts only at matched duty conditions or through the applicable manufacturer performance curves. OCP’s Liquid to Liquid CDU Test Methodology and Performance Rating, revision 1.0, ties thermal reporting to facility water system (FWS) and technology cooling system (TCS) conditions [S1]. Record entering FWS temperature, TCS supply and return, both flows, fluid identities and concentration basis, approach, available TCS head, FWS pressure drop, pump mode and control setpoints.

Establish independently measured heat offered to the boundary and the available load ceiling. A source supplying only 975 kW cannot prove a 1,000 kW capacity shortfall: the higher duty remains untested. A part-load measurement needs an applicable manufacturer performance model before extrapolation to a higher duty [S1, S8].

Which authority sets the acceptance limit?

The purchased duty sets required capacity; the accepted test procedure sets operating tolerances and the authorized acceptance signatory. Equipment documentation supplies model-specific performance conditions and operating limits. Agree the decision rule before the witnessed run, including action when the uncertainty interval crosses the minimum, following the conformity concepts in JCGM 106:2012 and ILAC-G8:09/2019 [S4, S5].

Keep chiller plant startup and commissioning as upstream readiness evidence; a chiller tolerance does not establish a CDU tolerance.

How do you calculate heat carried by the coolant?

Anvilfield’s single-phase heat-balance worksheet multiplies mass flow by coolant specific heat and return-minus-supply temperature. Using kg/s, kJ/(kg K) and K gives kW. Convert volume flow to mass flow using density at the meter’s fluid condition [S3, S10, S11].

Method: Q = m_dot × (h_return − h_supply) ≈ m_dot × cp_mean × (T_return − T_supply); m_dot = rho_at_meter × V_dot. Return-minus-supply makes secondary heat pickup positive. Here Q is thermal power, m_dot is mass flow, h is specific enthalpy, cp is specific heat, rho is density and V_dot is volume flow. Use enthalpy when temperature-dependent properties or pressure effects matter.

Capacity delta-T compares two locations on one stream. OCP revision 1.0 defines approach as TCS supply temperature minus FWS supply temperature [S1].

Calculate each synchronized sample’s heat before averaging. Multiplying average flow by average delta-T drops their covariance; use sample-specific properties or enthalpy where those properties change appreciably. This applies JCGM 100:2008, §4.1 [S3].

Where do you draw the measurement boundary?

Draw the exchanger, instruments, pumps, tank, bypasses and connection planes. Locate each heat source inside or outside that boundary and assign each correction a sign.

Account for pump energy entering the coolant and storage during ramps. Subtracting all CDU electrical input assumes every electrical watt becomes coolant heat inside the boundary, which requires evidence. Likewise, IT nameplate power and a load-bank setting do not measure coolant heat: retain electrical measurements and account for room-air and other heat paths.

Use load-bank acceptance criteria to define the applied load and liquid cooling loop commissioning to locate distribution and bypass boundaries.

Which coolant properties belong in the worksheet?

Use the actual fluid product, verified concentration and stated mass or volume basis. Dow’s DOWFROST LC Engineering and Operating Guide, Form 176-01641-01-0222, supplies the following typical values at 35°C [S10]. Anvilfield estimates the heat column at identical mass flow and temperature rise.

Anvilfield estimates that using LC 25 specific heat for an LC 55 stream overstates heat by 16.42%, calculated as (3.90/3.35 − 1) × 100 at these conditions.

Dow identifies these as typical properties, so its table does not supply a certified property uncertainty. The worked budget selects a 0.50% standard property allowance; replace it with supported concentration, temperature, tabulation and model information for the job. The coolant chemistry and concentration guide covers fluid identity and concentration control.

For water, IAPWS SR6-08(2011) provides thermodynamic correlations from 253.15 to 383.15 K at 0.1 MPa, including metastable regions; §6 discusses extension from saturation pressure to 0.3 MPa [S11]. Use a pressure-appropriate property formulation outside that scope.

How does flow uncertainty change the capacity result?

A 1% flow bias causes a 1% capacity bias with other inputs fixed, directly from the heat-balance equation. Identify whether the reading is mass or volume flow, and whether its specification is percent of reading or percent of span. The latter becomes a larger percentage of actual flow as the reading falls.

Endress+Hauser's Promag 50L technical information TI00097D/06/EN/18.16 specifies a pulse-output error limit of ±(0.5% of reading + 1 mm/s), which Anvilfield estimates as ±1.50% at 0.1 m/s and ±0.60% at 1 m/s under the stated reference conditions [S6].

Table C gives Anvilfield conversions of the standard and optional error formulas in TI00097D/06/EN/18.16, page 12. They are maximum-error bounds under its water reference conditions, typically 15 to 45°C and 0.5 to 7 bar. The current output adds typically ±5 μA; include the output path actually logged. The Promag document requires at least 5 DN upstream and 2 DN downstream, with a full pipe and suitable grounding and orientation [S6]. Apply another model’s own manual to its installation.

Bubbles, flow profiles, fluid mismatch, cutoff, scaling and analog conversion belong in the installed chain; retain hydronic balancing evidence.

A clamp-on ultrasonic meter is usable when its complete installed chain meets the budget. Retain pipe diameter, wall and liner data, fluid sound-speed setup, coupling, path and signal quality; verify at the intended fluid and flow against a suitable reference. For a BMS channel retain transmitter span, scaling, output and logger evidence.

How do you convert specifications to standard uncertainty?

NIST TN 1297 (1994) converts reported expanded uncertainty to standard uncertainty by dividing by its coverage factor: u = U/k [S2]. For a justified rectangular distribution bounded by ±a, use u = a/√3. Thus the ±0.60% bound at 1 m/s gives a 0.35% standard contribution under that selected distribution, before additional installed effects.

Correct known bias and retain uncertainty of the correction. Use certificate evidence for the effects it characterizes, retaining separate allowances for drift and installation. Under a uniform rounding model, display increment d contributes d/√12 standard uncertainty, separate from accuracy [S3].

Why does the temperature pair usually control low-delta-T tests?

Anvilfield estimates that a 0.10 K temperature-pair bias changes CDU capacity by 5% at a 2 K coolant rise, 2% at 5 K and 1% at 10 K, with flow and fluid properties held fixed. Correct differential bias before averaging.

Anvilfield estimates these sensitivities with the same absolute block-mean uncertainty at each delta-T.

Characterize both complete channels: probe, wiring, transmitter, logger and installed thermal contact. Compare them in a stable bath against a traceable reference at temperatures spanning the operating band. Retain each channel’s error versus temperature, reference uncertainty, bath uniformity and stability, and the differential uncertainty for the actual supply/return combination [S3].

Same-temperature agreement leaves gain error across a 30°C/40°C pair unresolved. Calibrate across the operating band and retain installed immersion/contact effects separately. Absolute channel errors still matter for supply-temperature and approach limits, even when an offset cancels in delta-T.

For the Anvilfield correction example, return indicated-minus-reference error is +0.06 K and supply error is −0.04 K. The indicated difference is therefore high by 0.10 K: subtract 0.10 K from 10.10 K to report 10.00 K, then retain uncertainty of that correction [S2].

WIKA operating instructions 3370964.13, 07/2026, give Class A element tolerance as ±(0.15 + 0.002 × |t|)°C [S7]. Anvilfield estimates ±0.21°C at 30°C and ±0.23°C at 40°C, allowing opposing errors totaling 0.44 K, or 4.40% of a 10 K rise. This is an element-error bound; the manual also excludes Class A and AA for its described two-wire connection.

When do common errors cancel, and when do they remain?

The uncertainty of a difference includes both channel variances and subtracts twice their covariance: u²(deltaT) = u²(Treturn) + u²(Tsupply) − 2 cov(Treturn, Tsupply) [S3, §5.2]. Anvilfield estimates 0.07 K differential standard uncertainty for equal 0.05 K inputs with zero correlation, versus 0.03 K at correlation 0.8.

A shared additive offset can cancel; unequal gain, immersion and response errors remain. Shared calibration equipment does not establish perfect correlation. The worked budget uses directly characterized pair uncertainty, so adding individual probe calibration terms again would double-count that evidence.

How do you build an auditable uncertainty worksheet?

Start with the decision margin. Anvilfield estimates that an expected 975 kW against a 950 kW minimum allows at most 25 kW expanded uncertainty, or 2.56%, under the lower-endpoint rule below. At k = 2, the combined standard uncertainty ceiling is 12.5 kW. Reserve part of that allowance for properties, installation and within-run variability before specifying instruments.

Convert every input to standard uncertainty, multiply it by the capacity sensitivity to that input, then combine the resulting contributions. JCGM 100:2008 permits root-sum-square combination for independent contributions and requires covariance terms for correlated inputs [S3]. In symbols: uc²(Q) = Σ[ci²u²(xi)] + 2Σi<j[ci cj cov(xi,xj)], where ci = ∂Q/∂xi.

All selected input uncertainties in this table are Anvilfield calculation inputs. The four Type B terms are modeled as independent normal inputs with well-established standard uncertainties; the block mean is approximately normal under the independent-block model. Replace the Type B degrees-of-freedom and distribution assumptions with job evidence.

Count drift, immersion, resolution and response mismatch once. Normalize temperature uncertainty by delta-T in kelvin, never by the Celsius supply reading. NIST TN 1297 (1994), §6 and Appendix B, supports approximately 95% coverage at k = 2 under applicable distribution and degrees-of-freedom conditions [S2]. A small-sample Type A dominated result needs an appropriate t factor.

What changes with a volumetric meter?

Divide liters per minute by 60,000, then multiply cubic meters per second by meter-condition density. This Anvilfield variant replaces the mass-flow row and retains the other terms.

The selected 0.35% installed volume-flow allowance is separate from the Promag bound conversion. When concentration or temperature drives both density and specific heat, propagate those common inputs or their covariance instead of assuming independent properties [S3].

Volumetric method note: V = 25 × 60000 / 1029.3 L/min before rounding; U/Q = 2 × √[0.0035² + 0.0020² + 0.0050² + (0.05² + 0.02² + u_mean²)/10²]. The variant uses independent normal volume-flow and density inputs.

How long should you stabilize and how often should you sample?

Anvilfield’s proposed protocol uses a 10-minute accepted steady window after stabilization, with synchronized samples at 1-second intervals and ten initial one-minute blocks. Extend the run for slow storage, sensor response or persistent correlation. These are Anvilfield protocol choices dated 2026-11-05, not an OCP test-duration requirement.

Calculate sample-wise heat first, then block means of heat. Use independent blocks or a suitable time-series method to estimate uncertainty of the steady-state mean. Delta-T scatter suffices for the worked dataset because flow and specific heat are fixed; on a varying run, adding separate flow, temperature and heat repeatability terms can count the same fluctuations more than once.

JCGM 100:2008, section 4.2.7, warns that time-correlated observations can invalidate the ordinary independent-sample estimate of uncertainty in the mean, so 600 logged readings do not automatically count as 600 independent measurements. NIST’s autocorrelation guidance supplies a diagnostic for temporal dependence [S3, S12]. Retain the correlation check and block-duration justification. Ten blocks alone provide weak evidence of independence; extend the record or repeat plateaus when needed.

What do you do with load steps, outliers and BMS data?

Split steady plateaus from load steps, control transients and failover recovery. Predefine window selection and retain every raw row with event flags. A valid excursion restarts the window; deleting it to pass a stability gate biases the result. Verify actual update timestamps and smoothing through BMS point verification. Polling a slow channel every second reproduces values without creating new independent evidence.

Separate clock alignment from fluid transport time. Compare common steady operating windows; during a transient, account for transport and stored energy through the boundary model. Keep recovery proof in integrated systems testing; a timestamp shift alone cannot establish steady energy balance.

Worked dataset: what does a 975 kW result prove?

Anvilfield’s worksheet v1.1, dated 2026-11-05, uses LC 25 at 25 kg/s, mean 30°C supply and 40°C return, and midpoint specific heat of 3.90 kJ/(kg K) from Dow’s 2022 guide [S10]. Each row is a selected one-minute block-mean input, treated as independent for this calculation.

Anvilfield estimates 975 ±18 kW, with k = 2 and approximately 95% coverage, for the stated LC 25 worksheet budget; its 957.2 to 992.8 kW interval, shown to one decimal place, demonstrates a 950 kW minimum under the page's agreed lower-endpoint rule.

Reproducibility method note: s_deltaT = 0.0666666667 K; u_mean = s/√10 = 0.0210818511 K. The five standard contributions are 4.875, 4.875, 4.875, 1.95 and 2.0554804791 kW. Their root-sum-square is 8.9064232439 kW; doubling gives 17.8128464879 kW, or 1.8269586141%. Welch-Satterthwaite evaluation, with only the block term assigned finite degrees of freedom, gives approximately 3,173 effective degrees of freedom.

Property-model method note: the allowance includes concentration, tabulation and approximation effects. Dow lists specific heat as 3.89 at 30°C, 3.90 at 35°C and 3.92 at 40°C [S10]. Piecewise-linear integration gives effective specific heat 3.9025 kJ/(kg K) and heat 975.63 kW, an Anvilfield sensitivity check 0.06% above the midpoint result.

Which upgrade improves the result fastest?

At 10 K, Anvilfield estimates that improving only standard flow uncertainty from 0.50% to 0.20% lowers expanded capacity uncertainty to 1.58%. Improving only pair calibration from 0.05 K to 0.02 K gives the same result. At 2 K the pair term dominates: improve differential characterization, installation and synchronization first, changing operating delta-T only within the approved duty.

How closely should the two heat balances agree?

Compare a boundary-corrected residual with its own uncertainty. Subtract measured TCS load and known internal heat additions from heat leaving to FWS, then account for storage and losses with their physical signs. For an exchanger-only steady boundary, compare FWS gain with TCS loss; an external pump does not belong inside that residual.

Anvilfield estimates the residual uncertainty by combining the three independent standard contributions in quadrature. The resulting interval includes zero. Establish the 5 kW net addition separately from the two thermal results and document its sign.

Apply JCGM 100:2008 covariance treatment when balances share probes, flow standards or coolant-property models [S3]. Correlated agreement supplies weaker independent corroboration and can conceal shared bias. An interval excluding zero directs investigation toward bypasses, scaling, signs, timing, pump heat, pipe heat exchange and storage before exchanger degradation; closure alone establishes neither rated duty nor sensor accuracy.

Does the CDU pass if the interval overlaps the requirement?

Use the agreed rule. Anvilfield proposes three outcomes for a specified minimum: demonstrated when the lower endpoint meets the minimum; demonstrated below when the upper endpoint is below it and the duty was properly exercised; overlap otherwise. This adapts decision-rule concepts from JCGM 106:2012 and ILAC-G8:09/2019 [S4, S5]. Neither document mandates this CDU rule.

A confidence interval from block scatter excludes calibration and other Type B components. Report the expanded measurement interval and coverage model. Keep the owner’s tolerance and decision risk separate from instrument uncertainty; a one-sided rule needs its own specified factor and risk model rather than silently reusing a two-sided k = 2 calculation.

Use unrounded worksheet endpoints for marginal decisions.

Is low capacity real, or is the measurement wrong?

Confirm fluid identity and equation units, verify flow scaling, compare temperature channels, then check bypasses, mixing and stability. Next match the rating conditions and available head. This sequence separates property and measurement errors from an exchanger or hydraulic limitation [S1, S3, S6, S10].

A rising approach at matched load and flow, after accounting for measurement changes, supports an exchanger investigation. Compare before-and-after results using uncertainty of the difference, including covariance from reused sensors and standards [S3]. Overlapping individual intervals alone do not settle whether performance changed.

Aggregate heat transfer can remain acceptable while one rack lacks flow. Resolve branch and node delivery through loop commissioning and hydronic balancing. Retain redundant-state capacity and recovery tests separately under liquid cooling redundancy; steady thermal proof closes only the condition measured.

What should the test scope cost and when should instruments be recalibrated?

Anvilfield estimates $3,500 for one day of measurement and a subsequent analysis allowance at one duty point, using the selected 2026 inputs below and assuming usable ports and load. Quote piping modifications, liquid load-bank provision, energy, plant operation, travel and shutdown arrangements separately.

Budget the eight-hour field shift as three hours for setup, two for readiness and operating conditions, and three for testing and export. Stabilization ends when the measured gates pass.

Write access, fluid checks, complete temporary measurement chains, certificates, logging, stabilized duties, witnessing, uncertainty calculations, exclusions and reruns into the bid scope. Estimators seeking public cooling work use PorchRocket Bid Control for HVAC bids and early signals from board meetings, budgets and capital plans.

ILAC-G24/OIML D 10:2022 bases recalibration interval selection and review on risk, drift, use, environment, intermediate checks and calibration history [S9]. Set pre-run and post-run pair and zero checks as field practice. These sources supply no universal annual instrument-calibration or full-load CDU retest requirement.

ILAC-G24/OIML D 10:2022, §§4.8 to 4.10, calls for retained calibration history, intermediate checks and results within predetermined limits before further instrument use [S9]. Anvilfield’s field practice also retains as-found/as-left results and reviews affected tests after a failed post-run check. Recalculate recoverable results; otherwise rerun.

Plan another capacity test after changes to the exchanger, fluid, pump arrangement or measurement chain that invalidate the baseline, or when a performance trend crosses the agreed action limit.

Field checklist and turnover record

Keep raw data, analysis and decision together. Correct failed checklist readiness items before another accepted window; follow the agreed rule for overlap.

1. Identify CDU serial/model, as-built revision and test mode; attach the purchased duty and actual OEM performance curve. If the operating point differs, label the tested duty explicitly.
2. Draw FWS and TCS measurement boundaries, bypasses, pump positions and thermal storage. Assign each heat correction to one boundary and one sign.
3. Identify fluid product, lot and concentration with mass/volume basis; record test-temperature property sources and uncertainty allowance. Resolve wrong or unverified fluid before calculating capacity.
4. Record all probe, flowmeter, transmitter and logger serial numbers, ranges and units; attach certificates with corrections, uncertainty, coverage factor and calibration date.
5. Verify full pipe, flow direction, straight runs and grounding against the meter's own manual. Correct the installation before using its specified error limit.
6. Compare both temperature channels against a traceable reference at multiple temperatures across the test band; retain corrections and a differential residual. Check installed immersion/contact and repeat after the run.
7. Verify timestamps, actual sensor update rate, scaling and unrounded data export. Correct stale points or mismatched units before accepting an interval.
8. Establish the specified duty, adequate applied load and pump state. Log the defined window, project operating limits and proposed stability metrics; flag excluded rows with reasons.
9. Calculate sample-wise heat, block values and the within-run component using a justified treatment of correlation. Extend the run if the effective evidence is insufficient.
10. List every correction and uncertainty component once; record covariance or the evidence for independence. Include the property model and installation effects.
11. Calculate capacity, standard and expanded uncertainty, k, coverage assumptions and any effective degrees of freedom. Apply the pre-agreed acceptance rule at the actual duty.
12. Compare independent FWS/TCS balances with boundary corrections. Investigate an unexplained residual outside its interval.
13. Retain the raw dataset, analysis version, formulas, accepted windows, as-found/as-left certificate files, pre/post-run checks and decision in one package. Retain witness and organization signoff.
14. Retain separate rack-flow, transient and redundancy results; a steady aggregate capacity result closes only the criterion it measured.

Retained dataset fields

Export these fields with unchanged units, corrections and revisions; link budget evidence by document and channel identifiers.

test_id, CDU_model, serial, duty_id, applied_heat_kW, available_load_limit_kW, required_conditions, actual_conditions, pump_mode, timestamp_UTC, actual_channel_timestamp, channel_id, location, unit, raw_value, correction, corrected_value, fluid_product, concentration_value, concentration_basis, property_revision, meter_fluid_temperature, density_at_meter, cp_model, accepted_window, exclusion_reason, block_id, Q_kW, calibration_document_id, u_standard, distribution, divisor, sensitivity, covariance_group, uc_kW, k, U_kW, coverage_basis, minimum_capacity_kW, decision_rule, outcome, analysis_version

Sources checked and page reviewed 2026-11-05. Update log: 2026-11-05: Worksheet v1.1; source recheck, calibration guidance, sampling controls and final editorial review.

Dataset citation: Anvilfield, “Worked dataset and uncertainty budget,” reviewed 2026-11-05, uncertainty budget, based on JCGM 100:2008, NIST TN 1297 (1994), and Dow Form 176-01641-01-0222 (2022).

How to cite this page: Anvilfield, How accurate is a CDU capacity test? A measurement uncertainty worksheet, 2026, https://anvilfield.com/field-guides/datacenter/data-center-cooling-capacity-measurement-uncertainty/.

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Sources checked

• [S1] Open Compute Project, Liquid to Liquid CDU Test Methodology and Performance Rating, Revision 1.0 §§3.3.2.1 to 3.3.2.4: reporting advice; footer August 2024, version table 11/01/2024.
• [S2] NIST Technical Note 1297, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, 1994 edition §§3 to 7, Appendix B: uncertainty framework.
• [S3] JCGM 100:2008, Evaluation of measurement data: Guide to the expression of uncertainty in measurement §§4 to 6: model, dependence, covariance.
• [S4] JCGM 106:2012, The role of measurement uncertainty in conformity assessment §8: decision risk.
• [S5] ILAC-G8:09/2019, Guidelines on Decision Rules and Statements of Conformity §§2 to 4: conformity rules.
• [S6] Endress+Hauser, Proline Promag 50L Technical Information, TI00097D/06/EN/18.16 pp.12 to 15: errors, installation.
• [S7] WIKA, Operating instructions TR10-L, TC10-L, TR10-0, TC10-0 (Ex d), document 3370964.13, 07/2026 pp.29 to 30: tolerance, wiring.
• [S8] Vertiv, Liebert XDU1350 Application and Planning Guide, SL-70618 Rev B, 07-22 Table 4.1, chapter 5: ratings, curves.
• [S9] ILAC-G24:2022 / OIML D 10:2022, Guidelines for the determination of recalibration intervals of measuring equipment §§4.8 to 6: retained results, intermediate checks and recalibration intervals.
• [S10] Dow, DOWFROST LC: Engineering and Operating Guide, Form 176-01641-01-0222 S2D, ©2022 Tables 2 and 3: typical properties.
• [S11] IAPWS SR6-08(2011), Revised Supplementary Release on Properties of Liquid Water at 0.1 MPa, September 2011 §§2, 6, 7: water-property scope.
• [S12] NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.12, Autocorrelation, undated web edition accessed 2026-11-05 Temporal-dependence diagnostic.