How to calculate flared port length

This is a routinely asked question:

"How long does the vent tube need to be if I use an n" flared port?"

Granted, there are a few calculators out there that will calculate this for you, particularly if you're using some of the widely available manufactured ports. Here's a good example of a calculator available to you:

Port Length Calculator

But what if you have hand-formed your flared ends? Better yet, let's assume you are a dork like me and prefer to hand calculate a lot of things (believe it or not, the extra effort is worthwhile in the long run, but that's a rant for another day).

Without getting too into depth on the actual derivation of the formula, here's what you need to know.

Where:

Lv = length of the vent tube (in meters)

N = number of ports (unitless)

c = speed of sound (in meters/second)

Rm = mouth radius of the flare (in meters)

Rt = throat radius of the flare (in meters)

Rf = flare radius (in meters)

Fb = frequency of port resonance (in Hertz)

Vb = size of enclosure (in cubic meters)

V = Volume of air in the flare

Rm = Rf + Rt

and

V = pi*Rf*Rm*Rm - (pi*pi*Rm*Rf*Rf/2) + (2*pi*Rf*Rf*Rf/3)

and for a vent with two flared ends:

Lv = N*c*c*Rt*Rt / (4*pi*Fb*Fb*Vb) - 0.85*Rm - 0.613*Rm - 2*V / (pi*Rt*Rt)

and for a vent with one flared end:

Lv = N*c*c*Rt*Rt / (4*pi*Fb*Fb*Vb) - 0.85*Rm - 0.613*Rt - 2*V / (pi*Rt*Rt)

I KNOW you are happy to have a lot of equations thrown at you, but this is actually relatively simple to sort out, as far as equations go. First, let's fill in the blanks I know the answer to in our simulation. We'll assume I have already measured or calculated the radius of the flare, throat, and mouth.

Lv = length of the vent tube (in meters)

N = 1 port

c = 340 m/s at sea level

Rm = mouth radius of the flare (in meters)

Rt = 0.05m (approximately 2 inches)

Rf = 0.025m (approximately 1 inch)

Fb = 10 Hz

Vb = 0.284m^3 (approximately 1 cubic foot)

V = Volume of air in the flare

As you can see, we are down to only three things that need solving! First, let's solve for Rm. As mentioned previously:

Rm = Rt + Rf

Rm = 0.05m + 0.025m

Rm = 0.075m

Now we move on to solving for V. This one is a bit more complicated, but still easy when we know all of the variables.

V = pi*Rf*Rm*Rm - (pi*pi*Rm*Rf*Rf/2) + (2*pi*Rf*Rf*Rf/3)

V = 3.14*0.025*0.075*0.075 - (3.14*3.14*0.075*0.025*0.025/2) + (2*3.14*0.025*0.025*0.025/3)

V = 0.0004415625 - 0.000231084375 + 0.0000327083

V = 0.0002432

Ok, now we're getting somewhere! Let's get to solving for Lv where both ends are flared!

Lv = N*c*c*Rt*Rt / (4*pi*Fb*Fb*Vb) - 0.85*Rm - 0.613*Rm - 2*V / (pi*Rt*Rt)

Lv = 1*340*340*0.05*0.05 / (4*3.14*10*10*0.284) - 0.85*0.075 - 0.613*0.075 - 2*0.0002432 / (3.14*0.05*0.05)

Lv = 289 / 356.704 - 0.06375 - 0.045975 - 0.0004864 / 0.00785

Lv = 0.81020 - 0.06375 - 0.04597 - 0.06196

Lv = 0.63852m

Lv = 25.15"

At last, we know how long the vent tube must be. There is one last step which you might find interesting.

Let's say you model up an enclosure (who hasn't?). Using a straight port with a 2" radius, you notice that the vent speed is approximately 15m/s. What will be the new vent speed, now that we have flared ports? Using the values for Rt and Rm that we determined previously, we can easily calculate the change in exit velocity.

Vt = 15m/s

Vm = Rt*Rt*Vt / Rm*Rm

Vm = 0.05*0.05*15 / 0.075*0.075

Vm = 0.0375 / 0.005625

Vm = 6.67m/s

That's quite a change! From % perspective standpoint, that's a decrease of approximately 56%!

Hopefully you enjoyed the little math lesson. Whether this is practical for you to learn in depth or not, it is definitely worth reading and maybe picking up some theory. If someone asks you any questions about calculating flared ports, you can answer intelligibly.