Dear Issam,

Regarding your question, first of all, v_tip represent the speed of fan blade tip point, so, it is a function of N(RPM). v_tip=Pi*d_tip*(N/60).

On the other hand, v_avg represents the velocity of air [m/s].

" I need an equation that links ΔPfan,rise with fan tip speed (or fan RPM)."

It is already mentioned!

ΔP_fan,rise=function of v_tip (RPM) & v_avg.

One more thing would like to withdraw your attention to, v_avg in this work would be obtained  by 4, 18 MP-AF

"Airflow measurement probe (transmits input signals

to the controller for controlling the speed of the fans

to obtain the preset airflow rate)"

http://www.tasonline.co.za/toolbox/pump/powtip.htm

v_tip is measured in [m/s]

v_tip=π*d_tip*N/60 (4)

ΔP_fan,rise=ΔP_static+(0.5*ρ* v_2^2) (7)

ΔP_fan,rise=(0.5*ρ* v_tip^2)*ψ+(0.5*ρ* v_avg^2)

ΔP_fan,rise=(0.5*ρ* [π*d_tip*N/60]^2)*ψ+(0.5*ρ* [v'/A_fan]^2) (8)

v' is the volumetric flow

ψ=ΔP_static/(0.5*ρ* v_tip^2) (9)

substituting (9) in (8):

ΔP_fan,rise=(0.5*ρ* v_tip^2)*(ΔP_static/(0.5*ρ* v_tip^2))+(0.5*ρ* [v'/A_fan]^2)

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ΔP_fan,rise=ΔP_static+(0.5*ρ* [v'/A_fan]^2) (???)

here is the part which I can't understand.

" I need an equation that links ΔP_fan,rise with fan tip speed (or fan RPM)."

used fan is GL12B4 Comair Rotron

Max. Air Flow 150.0 CFM (4.24m³/min)

Static Pressure 0.486 in H2O (121.1 Pa)

Nominal Speed: 3200 RPM

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Thank you very much

Attachments of two datasheets for the used fan.

Does the curve in datasheet2.png give the answer?

Dear,

It is mentioned static pressure, and you need units in IS. I suppose that you are going to use this fan!

All the best.

Well if you intent to use simple solution then use actuator disc theory ..lead to very simple approximation of flow rate ,pressure difference and blade speed. Well another approiach is to use the mean diameter values. If however you need better and more accurate answer then you have draw velocity triangles at blade hub and blade tip . athe work your way through to find the effect on pressure difference.

A fan is used to create velocity (kietic energy) for comfort and pressure for flow.

Blowers and compressors are for that purpose.

Pressure energy or pressures developed is very very small and velocity is considerable but still in the comfort range only.

Fan diameter, rpm, configuration (inlet and outlet angles, speed) for axial flow configuration with elocity triangles will give you all the relations for for flow velocity and flow rate.

I go with the third option given by Mr.Mohamed Afifi of velocity triangles if you have the fan or its dimensional details. It is simpe and any standard text book can be referred.