Fluid Machinery & Hydraulic Systems Workbench

Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

Fluid Machinery & Systems: theory, method, and sources

This fluid mechanics workspace publishes 10 governing equations, 5 stated assumptions, 1 documented boundary, and 2 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

Ten modules cover pump and turbine power, system and pump curve intersection, affinity laws, net positive suction head, specific speed, series and parallel pump combinations, hydraulic cylinders, accumulators, and fan laws.

The operating point module solves the intersection of a quadratic pump curve with a system curve, which is the calculation that determines the flow a given pump will actually deliver rather than its rated flow.

Calculators and topics covered

pumps
turbines
hydraulics
fans
NPSH
pump curve
system curve
affinity laws
hydraulic cylinder

Core equations

\text{pump hydraulic power:}\quad \begin{gathered}P_{h} = \rho gQH\\\text{shaft power:}\quad P_{s} = \frac{P_{h}}{\eta }\end{gathered}

\text{turbine shaft power:}\quad P_{s} = \rho gQH \cdot \eta

\text{system curve:}\quad H_{\mathrm{sys}} = H_{\mathrm{static}} + kQ^{2}

\text{operating point:}\quad H_{0} - aQ^{2} = H_{\mathrm{static}} + kQ^{2}

\text{affinity laws:}\quad \frac{Q_{2}}{Q_{1}} = \left(\frac{N_{2}}{N_{1}}\right) \left(\frac{D_{2}}{D_{1}}\right)^{3},\; \frac{H_{2}}{H_{1}} = \left(\frac{N_{2}}{N_{1}}\right)^{2} \left(\frac{D_{2}}{D_{1}}\right)^{2},\; \frac{P_{2}}{P_{1}} = \left(\frac{N_{2}}{N_{1}}\right)^{3} \left(\frac{D_{2}}{D_{1}}\right)^{5}

\text{net positive suction head available:}\quad \mathrm{NPSH}_{a} = \frac{p_{\mathrm{atm}} - p_{v}}{\rho g} + z_{s} - h_{L} \frac{- V^{2}}{2 g}

\text{specific speed:}\quad N_{s} = \frac{N \sqrt{Q}}{H^{\frac{3}{4}}}

\text{hydraulic cylinder:}\quad F = pA,\; v = \frac{Q}{A},\; A_{\mathrm{annulus}} = \frac{\pi \left(D_{\mathrm{bore}}^{2} - D_{\mathrm{rod}}^{2}\right)}{4}

\text{accumulator energy:}\quad E = \frac{p_{1} V_{1} \left[\left(\frac{p_{2}}{p_{1}}\right)^{\frac{n - 1}{n}} - 1\right]}{n - 1}

\text{fan laws:}\quad Q \propto N,\; \Delta p \propto N^{2},\; P \propto N^{3}

Method and assumptions

Assumptions

Pump and system curves are represented by simple quadratic forms rather than manufacturer-tabulated data.
Efficiency is a single constant value and does not vary with flow across the operating range.
Affinity laws assume geometric similarity and constant efficiency, which holds only over a limited speed range.
NPSH available is compared to a required value that must come from the pump manufacturer; cavitation margin is not assumed.
Series and parallel combinations assume identical pumps and neglect interaction losses in the manifold.

Limitations and design boundaries

Educational screening calculations only. Real systems require verified fluid properties, calibrated coefficients, uncertainty analysis, applicable codes and standards, and qualified engineering review.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy

Çengel and Cimbala, Fluid Mechanics: Fundamentals and Applications
Munson et al., Fundamentals of Fluid Mechanics