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:<math> \rho </math> a közeg sűrűsége.
Az affinitási összefüggések olyan gépekre, melyek <math>\phi</math> mennyiségi tényezője és <math>\psi</math> nyomásszáma azonos:
: <math> \frac{ Q_1 \over \ }{Q_2} = { \left ( \frac {D_1 \over }{D_2} \right )^3 \frac {n_1}{n_2} </math> ,▼:<math> \frac{\Delta p_1}{\Delta p_2} = \frac {\rho_1}{\rho_2} \left ( \frac {D_1}{D_2} \right )^2 \left ( \frac {n_1} {n_2}\right )^2</math> ,
:<math> \frac{P_1}{P_2} = \frac {\rho_1}{\rho_2} \left ( \frac {D_1}{D_2} \right )^5 \left ( \frac {n_1}{n_2} \right )^3</math> .
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'''Law 1. With impeller diameter (D) held constant:'''
Law 1a. Flow is proportional to shaft speed: <ref name=pumpfun>{{cite web|url=http://www.pumpfundamentals.com/yahoo/affinity_laws.pdf|title=Affinity Laws|work=www.pumpfundamentals.com}}</ref>, <ref>{{cite web|url=http://www.airturbine.com/fanlaws.html|title=Basic Fan Laws - Axial Fan Blades|work=airturbine propeller company}}</ref>
: <math> { Q_1 \over \ Q_2} = { \left ( {N_1 \over N_2} \right )} </math>
Law 1b. Pressure or Head is proportional to the square of shaft speed:
: <math> {H_1 \over H_2} = { \left ( {N_1 \over N_2} \right )^2 }</math>
Law 1c. Power is proportional to the cube of shaft speed:
: <math> {P_1 \over P_2} = { \left ( {N_1 \over N_2} \right )^3 }</math>
'''Law 2. With shaft speed (N) held constant:''' <ref name=pumpfun />
Law 2a. Flow is proportional to the cube of impeller diameter:
▲: <math> { Q_1 \over \ Q_2} = { \left ( {D_1 \over D_2} \right )^3 } </math>
Law 2b. Pressure or Head is proportional to the square of impeller diameter:
: <math> {H_1 \over H_2} = { \left ( {D_1 \over D_2} \right )^2 }</math>
Law 2c. Power is proportional to the fifth power of impeller diameter:
: <math> {P_1 \over P_2} = { \left ( {D_1 \over D_2} \right )^5 }</math>
http://www.engineeringtoolbox.com/affinity-laws-d_408.html
where
* <math> Q </math> is the volumetric flow rate (e.g. [[Cubic feet per minute|CFM]], GPM or L/s),
* <math> D </math> is the impeller diameter (e.g. in or mm),
* <math> N </math> is the shaft rotational speed (e.g. [[rpm]]),
* <math> H </math> is the pressure or head developed by the fan/pump (e.g. ft or m), and
* <math> P </math> is the shaft power (e.g. W).
These laws assume that the pump/fan efficiency remains constant i.e. <math> \eta_1 = \eta_2 </math> . When applied to pumps the laws work well for constant diameter variable speed case (Law 1) but are less accurate for constant speed variable impeller diameter case (Law 2).
==References==
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