Calculating Air Flow for Axial Flow Fans

No.

(obtain the fan performance curve)

The formula you seek is often used in technical journals, such as Journal of Fluid Mechanics, and you may want to go to the library and find it in journal.

However, for a crude but rational approach to thinking about the problem, offer this view: the volume of air displacement can be derived from this formula:

Q-cfm = V_icN_iN_r

where Q is the answer you want, V_ic is the volume of air displaced by one Impeller [or Blade - if you like] per Circular-rotation, N_i is the number of impellers/blades in the fan, and N_r is the number of circular-Rotations per minute.

Now the calculation of the displaced-air volume is the most difficult to do. For one thing, the blades or impellers have have pitches or twists so the volume displaced is a function of this "twist". However, assuming that the volume of air displaced as a blade rotates the distance equal to its effective width on the base as V_b and the number of such width per Circular-rotation is equal C_w, then the volume of air displaced has the following form, V_ic = V_bC_w resulting in the formula becoming:

Q-cfm = V_bC_wN_iN_r

Now you have a general formula and you should be able to customize it for your problem. By the way calculation of V_b entails some Calculus of Integration and a good understanding of the twist as well as the variation of the twist from the tip of the impeller to the base of the impeller.

Now keep in mind that even if you do not derive your own, when you finally find the formula in the technical journals you would be able to break it down into these contributory features and therefore gain better understanding.

I hope this helps. Good luck

I should try to finish up the engineering analysis I started in the above message, with the following additional formulae:

Number of Circular-Rotations blade width Cw = π.D/(w.Cosθ)

where π is pi with the value 3.14^..., w is the width of the blade base, θ is the angle of slant of the blade when the unit is placed horizontally on a support with the direction of flow facing upwards, D is the diameter of the unit to which the blades are affixed;

Volume of air displaced with rotational displacement equal to blade base-width V_b is given by

V_b = 2z_m ∫f(x)dx

the integration being from 0 to L where L is the length of the blade, and z_m is the inter-blade distance, and f(x) is the blade profile about the center line of symmetry.

The formula therefore becomes something like this:

Q-cfm = (N_iN_r )₍ π.D/(w.Cosθ)). 2z_m ∫f(x)dx

f(x) for rectangular blades is easy to derive, however, for other geometries, the suggestion is to use calipers to measure the variations of distance from the center-line of blade symmetry along the entire length, and then using regression analysis construct the best-fit function f(x) and you are done.

Keep in mind though that this analysis assumes that the blade design is flat. In those cases where the blade design is not flat, and have pitches or 'twists' you will have to resort to Differential Geometry, and use the tool known as The Frenet-Serret Apparatus to transform the blade geometry into a flat blade in some Mathematical space. In that space the above equation will hold so you simply have to substitute the transformation relations for the variable 'x' in the f(x) and in 'dx'. Of course, you may no longer have a closed solution, in which case you may have to look to Numerical Methods of solution.

Though a crude approximation in calculating the value, I hope that this helps.

Good luck

Measure the speed of air at the outlet of fan in ft/sec

then measure the area of the duct.

use following formula to calculate the flow rate in CFM

Q = A*V*60

where

A= area of the duct in ft2

V=velocity of flow in ft/sec

You can read this article. you will get your answer..

Fans Law:

http://www.multi-wing.net/support/fan-laws/

Thanks

http://impactgroupusa.com