Illustrative c5 external hydraulic duty
213 kPa external; 238 kPa pump total; 2.61 kW pump inputmodeled
| Value kind | modeled — Interpret this value according to its displayed kind, scope, source, and as-of date. |
|---|---|
| Scope | All inputs are assumed for a closed, four-parallel-rack circuit, carrying the water-property flow from Chapter 5.1 : 320 kW liquid IT heat, 10.0 K rise, density 1.00 kg/L and heat capacity 4.18 kJ/(kg·K). Use unrounded flow throughout. Common supply-plus-return length is 20.0 m at 65.0 mm internal diameter and total fitting coefficient K = 6.00; each long rack branch has 20.0 m of 32.0 mm pipe and K = 8.00. Darcy friction factor is 0.0250 in every segment, assumed to isolate geometry from roughness and Reynolds-number selection. Each rack consumes 70.0 kPa, the dirty external filter 30.0 kPa and the long-branch balance valve 10.0 kPa. CDU internal loss is a separate 25.0 kPa. The short branch alternative has 10.0 m of the same pipe. Wire-to-water efficiency is 0.700. For the pump-curve illustration, shutoff head is 300 kPa and the quadratic curve is fitted to this computed design duty; one duty pump must meet the full flow. For NPSH, pump-suction static pressure is 300 kPa absolute at the impeller datum, vapor pressure 9.60 kPa, suction diameter 65.0 mm, gravity 9.81 m/s², manufacturer NPSHR 3.00 m and project margin 1.00 m. Suction pressure already includes fill, elevation and upstream losses. The alternative low-fill pressure is 30.0 kPa absolute; the larger common-header alternative is 80.0 mm. These are teaching selections bounded by this chapter, not surveyed dimensions or catalog curves. |
| As of | 2026-09 |
| Source | Guide calculation from expressly assumed teaching inputs. Primary reference supplies method or equipment context, not evidence that this design was built or tested. |
| Derivation | Decision: choose the CDU against external circuit loss, then verify total pump duty and suction margin. The inherited flow is 320/(4.18 × 10.0) = 7.66 L/s for the zone, or 115 L/min per rack. Use v = Q/(πD²/4): the common header runs at 2.31 m/s and each branch at 2.38 m/s. Darcy–Weisbach gives Δp = (fL/D + K)ρv²/2: 36.4 kPa common and 66.9 kPa for the long branch. Add the common path to one parallel rack path: 36.4 + 66.9 + 70.0 + 30.0 + 10.0 = 213 kPa external head . Adding all four branch losses would count parallel paths in series. The short branch’s pipe-and-fitting loss is 44.8 kPa, so its balance valve must consume 32.1 kPa to match the long path’s 66.9 + 10.0 kPa. Add 25.0 kPa internal CDU loss to obtain 238 kPa total pump differential. Pump electrical input is QΔp/η = 0.00766 m³/s × 238,000 Pa / 0.700 = 2.61 kW , using unrounded operands. That fits inside the separate 3.00 kW heat allowance in Chapter 5.6 . For x = Q/Qdesign, the assumed system is Δpsystem = 238x² kPa and pump is Δppump = 300 − (300 − 238)x² kPa; their intersection is x = 1, the computed 459 L/min duty. A real selection must supply its measured curve, efficiency, stable operating range and dirty-filter envelope. NPSHA = (pabs − pv)/(ρg) + v²/(2g) = (300,000 − 9,600)/(1,000 × 9.81) + 2.31²/(2 × 9.81) = 29.9 m , above the assumed 3.00 + 1.00 = 4.00 m requirement. Static lift is not added again to a closed-loop friction duty, and an already established suction pressure is not charged the same elevation or suction loss twice. This screens the stated duty only; repeat for the hottest fluid, minimum fill, transients and each pump combination. Select the 240 kPa-external-head teaching CDU in Chapter 5.6 ; the 200 kPa unit misses this circuit. Flip the pipe: an 80.0 mm common header drops its loss to 14.2 kPa and external demand to 191 kPa, making the 200 kPa unit eligible at additional pipe-space and installation cost. Flip the fill: at 30.0 kPa absolute suction, NPSHA falls to 2.35 m and fails. The exact pressure crossover is pv + ρg(4.00 m) − ρv²/2 = 46.2 kPa absolute at this flow; operating reserve must sit above it. The Hydraulic Institute’s explanation of ANSI/HI 9.6.1-2024 defines available and required NPSH and application-specific margin. This chapter owns the hydraulic method; Chapter 13.5 owns installed acceptance. |
| Review | checking…cadence-derived review 2027-01-03 · standard cadence |
| Recorded changes | none recorded |
| Claim id | p5-c5-external-hydraulic-duty |
Where the guide uses it
Not quoted in a chapter yet; it is kept in the curated register.
← Full numbers register — every date-stamped figure in the guide, with revision history.