Supply root = max(terminal total pressure + path losses). Inlet root = min(intake total pressure − path losses). Required fan total-pressure rise = supply root − inlet root. Each path includes its shared sections once. Quadratic tree: ΔPt = R(Q/100)²; Rseries = ΣR; Rparallel = [Σ(1/√R)]⁻²; Q = 100√(ΔPt/R).
Q = section volume flow (CFM); ΔPt = total-pressure loss or imposed pressure difference (in. w.g.). R is the supplied quadratic resistance on the displayed Q/100 basis, so its numerical value is tied to that normalization. Root and terminal pressures share a common datum.
- Path check
- Choose scheduled-flow pressure accounting, a fixed-quadratic pressure-driven tree, or a supplied-value comparison. Use compatible total-pressure references and the stated airflow basis. Choices: Trace a single-fan supply and return/intake schedule; Sum one path schedule; Compare two complete path totals; Solve airflow in a supplied fixed-quadratic tree.
- Schedule, flow basis and pressure reference
- Identify actual geometry/product loss sources at the design flows, common airflow reference and terminal total-pressure datum. Include endpoint static/velocity requirements and entry/exit losses once. A reference does not authenticate those data. Applies to Path check: Trace a single-fan supply and return/intake schedule.
- Single-fan schedule basis
- Confirm both sides of one fan, compatible flow and total-pressure data, complete nonleaking branch coverage and documented endpoint boundaries. Any density or flow-reference conversion must already be established. Choices: Not established; Complete single-fan schedule and compatible flow/pressure bases established. Applies to Path check: Trace a single-fan supply and return/intake schedule.
- Scheduled segments on both fan sides (ID, side, parent, child, flow CFM, total loss in. w.g.)
- One row per actual segment, no header. Side 0 = return/intake; side 1 = supply/discharge. Parent is closer to the fan on both sides; root 0 is that side’s fan pressure plane. Actual return air travels child to parent. Unique segment IDs and node IDs 1–10000; positive flow on one declared basis; nonnegative total-pressure loss at that actual design condition. No static-regain subtraction, merging, loops or unlisted extraction. At most 100 segments. Applies to Path check: Trace a single-fan supply and return/intake schedule.
- All terminal pressure boundaries (side, leaf node, design flow CFM, boundary total pressure in. w.g.)
- Every leaf needs one row, no internal nodes or duplicates. Use the same side numbering and flow basis as the segment table. All boundary total pressures share one reference; signed values are allowed. Zero is appropriate only if that actual selected boundary has zero total pressure. Include downstream requirements once; no automatic room/static/velocity-pressure conversion is made. At most 100 boundaries. Applies to Path check: Trace a single-fan supply and return/intake schedule.
- Fan performance point
- Required duty can be calculated without a fan point. To compare, provide actual fan total pressure at the same full scheduled flow; static pressure and TESP are different quantities. Choices: Calculate required duty only; Compare a documented fan total-pressure point. Applies to Path check: Trace a single-fan supply and return/intake schedule.
- Fan point airflow on the schedule basis (CFM)
- Must match the complete scheduled fan flow after any independently established reference conversion. No fan-curve interpolation or density correction is inferred. Applies to Path check: Trace a single-fan supply and return/intake schedule; Fan performance point: Compare a documented fan total-pressure point.
- Available fan total pressure at that point (in. w.g.)
- Actual total-pressure rise at the matching fan flow and density. Do not enter fan static pressure, TESP or a pressure at another flow. Applies to Path check: Trace a single-fan supply and return/intake schedule; Fan performance point: Compare a documented fan total-pressure point.
- Fan total-pressure point reference
- Identify the actual fan/curve or measurement, speed, density, complete airflow and total-pressure convention. The teaching point must be replaced for a real comparison. Applies to Path check: Trace a single-fan supply and return/intake schedule; Fan performance point: Compare a documented fan total-pressure point.
- Tree resistance, pressure-node and validity basis
- Identify actual coefficient sources, unchanged geometry/control state, matching air density and CFM reference, complete terminal/exit losses and the range supporting a pure quadratic model. All leaves must share zero total pressure on one datum; source points alone do not establish this model. Junction coefficients depending on the split require separate validation. Applies to Path check: Solve airflow in a supplied fixed-quadratic tree.
- Fixed quadratic tree applicability
- Positive passive resistances, compatible total-pressure nodes and one constant density/volume basis. Every branch is listed. All terminal/exit losses are included once and every leaf ends on the same zero total-pressure datum. No static offsets, active controls, leakage, loops, merges or unknown fitting coefficients. Choices: Not established; Complete fixed-quadratic tree and pressure/flow/range basis established. Applies to Path check: Solve airflow in a supplied fixed-quadratic tree.
- Inlet total pressure above common leaf datum (in. w.g.)
- Positive fixed pressure boundary at inlet 0. This is a conditional snapshot, not a fan operating point, fan static pressure or TESP. Leaf total pressures are all zero on this datum; do not substitute room static pressure without accounting for velocity and terminal/exit losses. Applies to Path check: Solve airflow in a supplied fixed-quadratic tree.
- Complete fixed-quadratic section tree (ID, parent ID, reference CFM, reference loss in. w.g., minimum CFM, maximum CFM)
- 1–100 rows, no header. Unique section IDs 1–10000 also name outlet nodes. Parent 0 = supplied inlet plane; other parents identify an actual upstream section. Enter positive total-pressure loss at its positive reference airflow and a documented positive flow interval containing that reference. Each R = loss/(reference CFM/100)² is fixed throughout that range. Reference points need not form a flow-balanced schedule; solved flows must. Include every actual terminal/exit loss once. Out-of-range results are withheld. Applies to Path check: Solve airflow in a supplied fixed-quadratic tree.
- Straight-duct loss (in. w.g.)
- At the design airflow and selected method. Applies to Path check: Sum one path schedule.
- Fitting loss (in. w.g.)
- Use source-based fitting loss at the matching airflow. Applies to Path check: Sum one path schedule.
- Filter loss (in. w.g.)
- Use pressure loss at the matching condition. Applies to Path check: Sum one path schedule.
- Coil loss (in. w.g.)
- Avoid double-counting losses included in another pressure reference. Applies to Path check: Sum one path schedule.
- Terminal loss (in. w.g.)
- Use actual product data where applicable. Applies to Path check: Sum one path schedule.
- Other series losses (in. w.g.)
- Include only compatible components on this same path. Applies to Path check: Sum one path schedule.
- Path A total (in. w.g.)
- Enter the complete compatible series total. Applies to Path check: Compare two complete path totals.
- Path B total (in. w.g.)
- Enter the complete compatible series total. Applies to Path check: Compare two complete path totals.
