[ciniva (OP)]

How can I calculate fan power in these two cases?

The first case is direct wind speed of 10 m/sec.
The fan diameter is 40 cm. The fan housing is shown in the figure.
How to calculate a number 'rpm per second'.

The other case is when the housing is a cone and the fan is 20 cm in diameter.

How to calculate the rotational strength?
In which case is the power of rotate higher?
Is there any formula in the calculation?

I found some formula P=1/2*p*a*V3
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[alancalverd]

The equation P = ½ρAv³ is correct. ρ is the density of air, A the area of the fanduct, and v the exhaust speed.

However this only calculates the power transferred to the air. To calculate the fan speed you need to know its efficiency, which is a  complicated and nonlinear function of the blade geometry and v. That said, if you assume 100% transfer at the optimum speed for a given fan, then the swept volume per second is Av and each blade sweeps  an area A ω times per second where ω is the rotation speed, so you can calculate ω for a fan with n blades.

[ciniva (OP)]

Hi @alancalverd
Thank you for your reply. This is a high science for me.
I do not know enough about all the relevant values or elements to know how to calculate the power.
Can you tell me, which option in the image above (upper or lower) has stronger power rotation.
Thanks in advance