A closed-form probabilistic framework for pump sizing in building water supply systems

Workflow for reliability-based pump sizing, from design inputs and modelling steps to operating point, reliability, power evaluation, and final pump selection. Conventional pump sizing in building water supply systems follows Hunter's Fixture Unit (FU) method, which deterministically assigns peak demand at approximately the 99th percentile. While conservative, this approach often leads to oversizing and operation away from the best efficiency point (BEP). This study introduces a probabilistic yet closed-form framework that reframes FU as a percentile demand model and extends it into a reliability spectrum. Fixture demand is represented by normal and lognormal distributions calibrated such that FU corresponds to the 99th percentile. Pump operating points are determined by the intersection of the system curve (Darcy–Weisbach, Colebrook–White, K-method) and polynomial-fitted pump curves, with BEP identified analytically. Hydraulic reliability is then computed directly from the demand cumulative distribution function (CDF). A representative case study demonstrates how the framework quantifies trade-offs between reliability and pump power. The method offers transparency, reproducibility, and practical decision support for engineers by linking catalogue pump selection with explicit reliability targets. Future extensions may incorporate variable-speed drives, multi-pump operation, and stochastic pipe parameters.