Derivation of air flow constant 4005? 1

[Leon95628]

I am looking for a derivation of the constant "4005" that is used in hvac vav's for air flow vs. velocity pressure in a round pipe. Q(cfm) = 4005 * aspect ratio * sqrt [velocity pressure (in h20)]

Thanks!!

 

[quark]

From Bernoulli's equation

(P1-P2)/Rho = V[sup]2[/sup]/2g (i.e static pressure difference creates flow)

1 lb/sq.ft = 0.1922 inches of wc
1g = 115820 ft/min[sup]2[/sup]

So V = [(2 x 115820)*dP/(0.075 x 0.1922)][sup]1/2[/sup]
i.e V = 4008.6 x dP[sup]1/2[/sup] (there may be some conversion problems for the costant to be high by 3.6)

Q = A x V (it is not aspect ratio here but the product of two sides)

Regards,





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[Leon95628]

Thanks very much!!

 

[25362]

According to manuals: 0.19255 in wg = 1 psf.

Thus

V = 4005 P[sup]0.5[/sup]​

 

[25362]

For the sake of units' consistency the gravitational conversion factor

g[sub]c[/sub] = 115826 (ft.lb[sub]m[/sub])/(min[sup]2[/sup].lb)​