Vent length recalculation formula

[arjscott]

I'm building a bass reflex enclosure that specifies a vent with a diameter of 65mm, and length of 75mm.

I have some 62mm pipe so I need to recalculate the vent length based on the smaller diameter.

I found two formulae in this post:

http://www.diyaudio.com/forums/showthread.php?postid=600466#post600466

The thread is quite old, so I decided to start a new one instead of replying in there.

L1 = original length
D1 = original diameter
L2 = new length
D2 = new diameter

The first one is pretty simple, and L2 looks sensible (68.23mm)

L2 = L1*(D2^2/D1^2)

The second one (according to GM) takes end correction into account. I don't understand the result of this calculation because the length works out to 77.2mm.

L2 = L1*(D2^2/D1^2)+(D2-D1)^2

I've tried entering several different diameters where D2 is smaller, and it always seems to work out longer. If the vent diameter is reduced, shouldn't the length be shorter?

Can someone with a better understanding of vent calculations (and maths!) explain what is happening here?

Am I repeatedly screwing up the calculation? Apologies in advance if I am missing something obvious.

 

[Ron E]

Length varies as area. If you double area, you double length.

Area of a circle varies as diameter squared.
L1/L2=(D1/D2)^2
L2=L1/(D1/D2)^2

L2=75/(65/62)^2=68mm

If you wish to take end correction into account - which isn't necessary in your case - just calculate the vent length the normal way.

Lv=2360*Dv^2/(Vb*Fb^2)-.73*Dv
(dimensions im mm, volume in liters)

 

[Notax]

Lv=(Rt*Rt*C*C)/(4*pi*Fb*Fb*Vb)-1.7*Rt

Rt=Dt/2 - half diametar (m)
C - speed of sound (m/s)
Fb - tuning freq. (Hz)
Vb - volume of box NETTO (m3)

All in SI metric, and you got Lv (m).


Lt2=(Rt2*Rt2)/(Rt1*Rt1)*(1.7*Rt1+Lt1)-1.7*Rt2

In this case:

Lt2=65.8 mm

 

[arjscott]

Thanks for the clarification, Ron E.

Notax: That formula looks interesting but actually understanding it is beyond my mathematical ability! I've had some fun making calculations with it anyway.