Run number

Physical key figure
Surname	Run number
Formula symbol	${\displaystyle {\mathit {\sigma }}}$
dimension	dimensionless
definition	${\displaystyle \sigma =n\cdot {\frac {2{\sqrt {\pi \cdot {\dot {V}}}}}{(2\cdot Y)^{3/4}}}}$
${\displaystyle n}$ Impeller speed ${\displaystyle {\dot {V}}}$ Volume flow ${\displaystyle Y}$ specific nozzle work
scope of application	Turbo machines

The running number (also called the high-speed number) is a dimensionless number for characterizing single-stage flow machines . It is the ratio of the speeds of a turbo machine and a comparison machine and plays a role similar to the specific speed . ${\displaystyle \sigma }$ ${\displaystyle n_{\rm {q}}}$

The running number is important for the design of turbomachines because it is plotted together with the diameter number in the Cordier diagram .

definition

The derivation of the running number is based on the definition formulas of the flow machine parameters flow rate and pressure number : ${\displaystyle \varphi }$ ${\displaystyle \psi }$

${\displaystyle \sigma ={\sqrt {\frac {\varphi }{\sqrt {\psi ^{3}}}}}}$

These are transformed in such a way that the diameter of the impeller is eliminated and the impeller speed is linear : ${\displaystyle n}$

${\displaystyle \Leftrightarrow \sigma =n\cdot {\sqrt {\frac {{\sqrt {2}}\cdot \pi \cdot {\dot {V}}}{\sqrt {Y^{3}}}}}}$

The volume flow of the impeller outlet and the specific nozzle work mean requirements that are placed on the turbomachine. ${\displaystyle {\dot {V}}}$ ${\displaystyle Y}$

Demarcation

To describe wind turbines that will speed ratio used. This indicates the ratio of the rotational speed of the blade tip to the wind speed .

literature

• Bohl, Willi; Elmendorf, Wolfgang: Turbo machines 1: Structure and mode of operation Vogel; Edition: 10th Würzburg 2008, ISBN 978-3834331304 , page 74
• Sigloch, Herbert: Fluid flow machines: Basics and application Hanser; Edition 5, updated edition; 2013 Carl Hanser Verlag Munich; ISBN 978-3-446-43242-0 ; Page 118