Four 7 inch socks or twelve 4 inch socks?

FishTruck · Jan 18, 2022

I am going to make a filter sock holder for a larger system. I have room for either four 7 inch socks, or, twelve 4 inch socks.
Assuming that they are the same lengths, the surface area of the sock walls is directly proportional to the radius. So....

4 x 7 = 28
12 x 4 = 48

So, I would have 1.7 x the surface area of filter material using the smaller socks versus the bigger ones. In practical terms, would this handle a larger water flow and hold more total detritus before clogging of the entire array? Seems obvious - but is there more to it?

Sshannon · Jan 18, 2022

Wait, I think there is more to the math. What is the diameter and length of each size sock, please?

Hendrix · Jan 18, 2022

Are you asking about 7" Length or Girth?

FishTruck · Jan 18, 2022

The diameters are 4 inches or 7 inches. In both cases the length would be 14 inches.

The area of an open cylinder is circumference x length. The socks are typically sewn together at the bottom without a flat disc, so no need to calculate the area of a circle.

Since the lengths cancel out, only the circumference changes with each sock. Formula for circumference is Pi x diameter.

Since Pi also cancels out, and there is no exponential math here, the ratio of area is the same as the ratio of the diameters of the socks, right? 4 to 7.

The real advantage is that I can fit twelve four inch socks in the same tray as four seven inch socks. Thus, the area of filter material in the two potential setups is proportional in the following way...

Four 7 inch socks = total circumference of 28 x Pi x length. Or, 4 socks x 7 inches diameter x 3.14 x 14 inch length = 1231 cubic inches.

Twelve 4 inch socks = total circumference of 48 x Pi length. Or 12 socks x 4 inch diameter x 3.14 x 14 inch length = 2110 cubic inches.

2110/1231 = roughly 1.7. So, I get 1.7 times the surface area of material running twelve four inch socks versus four seven inch socks in the same size filter sock tray.

Hendrix · Jan 18, 2022

I would use the largest diameter & longest length that u can..

I use (3) 7" on my tank (500g) - I rinse them every 3-7 days.

My tank is bare bottom and super low nitrate

FishTruck · Jan 18, 2022

The question I have... I running 1.7 x as much material going to translate into being able handle 1.7 x the flow? How about 1.7 x the detritus?

FishTruck · Jan 18, 2022

Hendrix said:
I would use the largest diameter & longest length that u can..

I use (3) 7" on my tank (500g) - I rinse them every 3-7 days.

My tank is bare bottom and super low nitrate

The long length makes sense.

Why the larger diameter? Easier to turn inside out. What else?

Hendrix · Jan 18, 2022

I understand your math & agree it may be more surface area.

What other metrics matter:
- Cost the 4" will cost you more to swap out
- the 4" will give you more to clean
- I like simple clean 4 vs 12

I clean mine before the clog up.

Hendrix · Jan 18, 2022

As I look at your photo in your profile, I can't help but say "Your gonna need a bigger sock". Chief Brody didn't say we need more smaller boats, did he?

embrace your brand
lol

Cell · Jan 18, 2022

I'd sacrifice a bit of surface area and have 8 less socks to change/maintain.

Bpp124987 · Jan 18, 2022

Three roller mats!

boacvh · Jan 18, 2022

Just being the devil's advocate here, and not an expert by any means, but I would argue the 4 - 7 inch would be greater than the 12 - 4 inchs. Socks are more like a cone than a cylinder. I wouldn't cancel the height and calculate volume or surface area. Basically, the volume of 4 cones with 14 inch heights and 7 inch diameters is > than the volume of 12 cones with 4 inch diameters and 14 heights. No?

FishTruck · Jan 19, 2022

Hendrix said:
As I look at your photo in your profile, I can't help but say "Your gonna need a bigger sock". Chief Brody didn't say we need more smaller boats, did he?

embrace your brand
lol

LOL

boacvh said:
Just being the devil's advocate here, and not an expert by any means, but I would argue the 4 - 7 inch would be greater than the 12 - 4 inchs. Socks are more like a cone than a cylinder. I wouldn't cancel the height and calculate volume or surface area. Basically, the volume of 4 cones with 14 inch heights and 7 inch diameters is > than the volume of 12 cones with 4 inch diameters and 14 heights. No?

The ones I have look like they take a rectangle of material, height by circumference, sew a circle on the top and a single seam on the bottom. I have seen some that are more conical (but pleated), and some that are truly cylindrical with a flat circle on the bottom.

Bpp124987 said:
Three roller mats!

I have two big roller mats already. Mixed feelings about them. They can't quite handle the full flow of my system, if I push them too hard, I find that I have eaten a whole roll of material over night (GRRR) and, due to some gravity issues mixed with poor planning, I can't plumb my grow out tanks into them. So... the socks I use to handle overflow from display, siphoning activities, and frag tanks.

Thanks Guys!

I think I will start with 7 inch socks, since I have them already. If I really get bored, I can easily cut holes in a new piece of PVC and try the 12 four inch socks. (It's just that I can fill up four 7 inch socks in about two days lately).