Flow rate

Physical key figure
Surname	Flow rate
Formula symbol	${\displaystyle {\mathit {\varphi }}}$
dimension	dimensionless
definition	${\displaystyle \varphi ={\frac {4\cdot {\dot {V}}}{\pi \cdot D^{2}\cdot u}}}$
${\displaystyle {\dot {V}}}$ Volume flow ${\displaystyle D}$ Impeller outer diameter ${\displaystyle u}$ Peripheral speed
scope of application	Turbo machines

The flow coefficient φ (also Delivery number or volume number ) is a dimensionless characteristic number describing the flow rate of fluid flow machines . It can be understood as the ratio of the volume flow at the outlet of the impeller to an imaginary volume flow, which is formed from the circular area of the outer diameter of the impeller and its peripheral speed : ${\displaystyle {\dot {V}}}$ ${\displaystyle {\frac {\pi }{4}}\cdot D^{2}}$ ${\displaystyle D}$ ${\displaystyle u}$

${\displaystyle \varphi ={\frac {4\cdot {\dot {V}}}{\pi \cdot D^{2}\cdot u}}}$

Using the impeller speed, the following can be formulated: ${\displaystyle n={\frac {u}{\pi \cdot D}}}$

${\displaystyle \Leftrightarrow \varphi ={\frac {4\cdot {\dot {V}}}{\pi ^{2}\cdot D^{3}\cdot n}}}$

Other definitions

By means of meridian velocity

In the past, the flow rate was defined by means of the meridian velocity at the impeller outlet as: ${\displaystyle c_{m}}$

${\displaystyle \varphi ^{\prime }={\frac {c_{m}}{u}}}$

Here, the meridional velocity the component of the flow velocity in not -mitrotierenden reference system , the orthogonal through the exit surface enters the impeller: . Therefore one can formulate: ${\displaystyle c_{m}}$ ${\displaystyle A_{2}}$ ${\displaystyle c_{m}={\frac {\dot {V}}{A_{2}}}}$

${\displaystyle \Leftrightarrow \varphi ^{\prime }={\frac {\dot {V}}{A_{2}\cdot u}}}$

For the mathematical formulation of the surface there are different formulas for the different impeller geometries of axial and radial machines. ${\displaystyle A_{2}}$

Regarding the inlet diameter

Since the absorption capacity of a machine depends on the entry area into the blade grille, it may be useful for certain considerations to relate the flow rate to the entry diameter of the impeller.

Cross-flow fan

Since the impellers of cross-flow fans flow through them transversely to their axis of rotation, it makes little sense to relate the flow rate to the circular area of ​​the outer diameter, because the flow rate can be increased almost arbitrarily by widening the wheel. For cross-flow fans, it is more useful to refer to the projected area of ​​the rotor.

literature

• Willi Bohl: Turbo machines 1, structure and mode of operation . Vogel, Würzburg 1998, ISBN 3802317378 .
• Bruno Eck: fans, design and operation of centrifugal, axial and tangential fans . Springer, Berlin 1991, ISBN 3540534946 .
• Herbert Sigloch: Fluid flow machines , basics and applications . Hanser, Munich 2009, ISBN 9783446418769 .

Individual evidence

1. ↑ Bruno Eck: Fans. Springer, Berlin 1991, p. 11.
2. ↑ Bruno Eck: Fans. Springer, Berlin 1991, p. 10.