Hydrostatic pressure again

[steveh2112]

hi, i know hydrostatic pressure has been discussed on this forum but I'm still not convinced (i know, crazy me)

i have a practical application actually.

i'm planning to build a bubble panel (a.k.a bubble wall). its like a tall, wide but very narrow fish tank but no fish, just bubbles.

i'd like to use standard (not tempered) 10mm window glass and the size of the tank will be 180cm high, 150cm wide and 1cm deep (front to back i mean) and i want to verify the glass is strong enough to hold back the water

hydrostatic pressure on the glass at a depth of 180cm is, according to http://www.engineeringtoolbox.com/ 0.18kg/cm2

so if i consider a strip of the bottom of the tank, 10cm high and 150cm wide (width of tank) that 1500cm2 x 0.18kg is 270kg. so that's a total of 270kg pressing on the glass on the bottom 10cm of the tank! is that right? (ok, i should have used the average depth of that strip of 175cm, but that's not my point)

270kg actiing on that strip doesn't make a whole lot of sense to me because the total weight of the water is 180*150*1 = 27,000cm2 which is 27 liters = 27kg

how can hydrostatic pressure exert more force than the weight of the actual fluid?



thanks, steve

 

[K^2]

You mean the force on the wall, right? That's because the force is horizontal. It is balanced by the force on the opposite wall. Only the net force on the bottom of the tank must equal the weight of the fluid. And if you look at your setup, it does. The 1cm * 150cm * 0.18kg/cm² = 27kg.

While it might seem counter intuitive that force on the walls can exceed weight of the fluid, think about what happens when you force a wedge into a crack. You can generate significantly higher forces outwards than force applied to the wedge. It's the same idea as you do with the lever. You get force advantage on distance disadvantage.

Where is the distance disadvantage? Well, imagine that the section of the wall, these 10cm x 150cm gave out and started moving outwards. If that section moves out by 1mm, how far does the water level drop? 10mm. Exactly 10x more. And that's exactly the 10x force advantage you are getting. Just like you do with a lever, gears, or a wedge.

 

[steveh2112]

wow, you have no idea how long that hydrostatic pressure thing has been bothering me. now i see it totally, thank you so much for the great explanation.

my guess is that i may have a problem with my tank design using 10mm glass. i expect the loading on the side walls will be very high.

but i think i can help it by putting intermediate connectors between the front and back walls like in this video http://www.youtube.com/watch?v=Fvu5j2M6ihQ&feature=related

or this http://www.youtube.com/watch?v=4caen4c6BDw&feature=related (pretty cool video this one)

thanks again

 

[K^2]

Well, there are probably some large, rectangular aquariums with one of the walls being close to 150cm wide by 180cm tall. The loading on these will be the same regardless of whether they are spaced 1cm or 300cm. So same thickness of glass should work. If you can find one somewhere with type of glass and thickness used, you'll have your answer.

Yes, connectors would significantly reduce the load on the walls. You have to be careful to not compromise structural integrity by cutting holes, though. Circular ones are definitely your best bet, as it reduces probability of cracks.

Also, I'd be surprised if they aren't using plexiglass. It's easier to cut holes in, glue together, and is less likely to crack. I'm not sure if it's actually stronger, but if you are going to have connectors, it'd almost certainly be a better choice.

 

[steveh2112]

plexiglass (acrylic sheet) is about 3x the cost of glass so i want to try glass first. my connectors will be glued in place so no hole cutting in the glass. i'll post a pic when my project is finished. thanks for the help.