HYD-28

Pump affinity laws

Q2/Q1 = n2/n1, H2/H1 = (n2/n1)², P2/P1 = (n2/n1)³ at constant diameter.

Reading speed

PumpsPump affinity

Governing equation

Q_2/Q_1=n_2/n_1,\quad H_2/H_1=(n_2/n_1)^2,\quad P_2/P_1=(n_2/n_1)^3

$n_2 \in \left[400, 3600\right]$

where

Q_1: Duty flow (L/s)
H_1: Duty head (m)
P_1: Duty power (kW)
n_1: Rated speed (rpm)
n_2: New speed (rpm)
Q_2: New flow (L/s)
H_2: New head (m)
P_2: New power (kW)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

Q_2/Q_1=n_2/n_1,\quad H_2/H_1=(n_2/n_1)^2,\quad P_2/P_1=(n_2/n_1)^3

$n_2 \in \left[400, 3600\right]$

$n_2 = 400$ $Q_2 = 11.03$

Along the curve

②

Domain of the variable — blue

n_2_{\min} = 400,\quad n_2_{\max} = 3600

$n_2 \in \left[400, 3600\right]$

$n_2 = 400$ $n_2 = 400$

Along the curve

③

Response curve — green

Q_2/Q_1=n_2/n_1,\quad H_2/H_1=(n_2/n_1)^2,\quad P_2/P_1=(n_2/n_1)^3

$n_2 \in \left[400, 3600\right]$

$n_2 = 400$ $Q_2 = 11.03$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Q_2}{\mathrm{d}n_2}

$n_2 \in \left[400, 3600\right]$

$n_2 = 420.1$ $Q_2^{\prime} = 0.028$

Along the curve

Lecture brief

Historical brief

Open-channel and pipe flow were written by Chezy, Manning, Darcy and Weisbach in the nineteenth century, then Bakhmeteff and Bélanger on the hydraulic jump. The sheets compute conveyance, head loss and gradually varied profiles. This sheet (HYD-28 — Pump affinity laws) is the form associated with Pump affinity. Working symbols: $Q_1$ , $H_1$ , $P_1$ , $n_1$ , $n_2$ $\rightarrow$ $Q_2$ , $H_2$ , $P_2$ . Dimensional similarity of a rotor. Cut-down diameter uses D in place of n with the same exponents plus extra D.

Purpose

Purpose: compute

Q_2

H_2

P_2

from

Q_1

H_1

P_1

n_1

n_2

in Hydraulics via

Q_2/Q_1=n_2/n_1,\quad H_2/H_1=(n_2/n_1)^2,\quad P_2/P_1=(n_2/n_1)^3

Q2/Q1 = n2/n1, H2/H1 = (n2/n1)², P2/P1 = (n2/n1)³ at constant diameter. Use it when a real hydraulics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Q_1 = 40.000\,\mathrm{L/s}

H_1 = 25.000\,\mathrm{m}

P_1 = 12.000\,\mathrm{kW}

n_1 = 1450.000\,\mathrm{rpm}

n_2 = 1200.000\,\mathrm{rpm}

, the governing relation

Q_2/Q_1=n_2/n_1,\quad H_2/H_1=(n_2/n_1)^2,\quad P_2/P_1=(n_2/n_1)^3

yields

Q_2 = 33.10\,\mathrm{L/s}

H_2 = 17.12\,\mathrm{m}

P_2 = 6.80\,\mathrm{kW}

. A pump curve, a speed change, a similar point. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Duty flow Q_140 L/sDuty head H_125 mDuty power P_112 kWRated speed n_11450 rpmNew speed n_21200 rpm

Outputs

New flow Q_233.10 L/s
New head H_217.12 m
New power P_26.80 kW

Reading speed

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Narration of this film

A pump curve, a speed change, a similar point.

Dimensional similarity of a rotor. Cut-down diameter uses D in place of n with the same exponents plus extra D.

Reading speed

Watch on YouTube