Hardy Cross Pipe Flow Calculator

Exactly one oriented single-loop Hardy Cross iteration, not shared-pipe network convergence or automatic balanced boundary flows. Caller independently establishes units, regime, calibration and applicability; this does not establish design-code compliance, authenticity, operational safety, treatment efficacy or a validated forecast.

Description

Hardy Cross adjusts an assumed pipe-loop flow distribution using head-loss imbalance.

Hardy Cross adjusts an assumed pipe-loop flow distribution using head-loss imbalance.^[1]

One correction is a numerical step rather than a converged multi-loop network solution. Use this tool to calculate hardy Cross Pipe Flow from the supplied measurements and assumptions.

When to use Hardy Cross Pipe Flow Calculator

Use this tool to calculate hardy Cross Pipe Flow from the supplied measurements and assumptions. Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.

How to use Hardy Cross Pipe Flow Calculator and understand its results

Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
Enter signedLoopFlowsM3Second, callerLoopResistance, callerHeadLossExponents, using the field meanings and rules below, then run the tool.
Read oneHardyCrossCorrectionM3Second, correctedSingleLoopFlowsM3Second. Interpret the fields using their units, signs and evidence conventions below.
If input validation fails, correct the reported field and run again. Before applying the result, check reference scope, model assumptions and any missing evidence or placeholder values.

Input field	Meaning	Value type	Requirement
signedLoopFlowsM3Second	Signed loop flows m3 second	list of number	Required
callerLoopResistance	Caller loop resistance	list of number	Required
callerHeadLossExponents	Caller head loss exponents	list of number	Required

Enter nonempty aligned finite signed loop flows, positive resistance coefficients and exponents from 1 through 3. Sum r×sign(q)×abs(q)^n and derivative r×n×abs(q)^(n−1), requiring positive derivative. Correction is minus head sum/derivative and is added to every signed loop flow. Only one loop step is performed; no network continuity repair or convergence iteration is provided.

deltaQ=−Σr_i×sign(q_i)×abs(q_i)^n_i / Σr_i×n_i×abs(q_i)^(n_i−1); corrected_i=q_i+deltaQ

Use the exact units, boundary rules, ordering and missing-evidence conventions above.

Output field	Meaning	Value type
oneHardyCrossCorrectionM3Second	One Hardy Cross Correction M3 Second; follow the units, sign, ordering and evidence convention stated above	number
correctedSingleLoopFlowsM3Second	Corrected Single Loop Flows M3 Second; follow the units, sign, ordering and evidence convention stated above	list of number

json

{
  "input": {
    "signedLoopFlowsM3Second": [
      2,
      -1
    ],
    "callerLoopResistance": [
      1,
      1
    ],
    "callerHeadLossExponents": [
      2,
      2
    ]
  },
  "output": {
    "oneHardyCrossCorrectionM3Second": -0.5,
    "correctedSingleLoopFlowsM3Second": [
      1.5,
      -1.5
    ]
  }
}

Limitations and assumptions

One correction is a numerical step rather than a converged multi-loop network solution. Interpretation depends on the units, sampling scope and exact model described above.

All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse evidence arrays fail validation; the specific bounds and alignment requirements are stated above. Extremely large inputs or outputs can also be rejected. An input error is distinct from a successful result reporting false, no matches or missing evidence.

Alternative or Complementary methods

Use Seepage Flow Net Calculator for this related task: A flow-net seepage estimate uses the ratio of independently counted channels and potential drops.

Use Sewer Self-Cleansing Velocity Calculator when its separate inputs and assumptions fit the question: A wall-shear relation connects a target shear stress with a Darcy friction factor and flow velocity.

References

Hardy Cross Pipe Flow Calculator — tool.io

Similar or alternative tools

Seepage Flow Net Calculator
A flow-net seepage estimate uses the ratio of independently counted channels and potential drops.
Sewer Self-Cleansing Velocity Calculator
A wall-shear relation connects a target shear stress with a Darcy friction factor and flow velocity.