This is the revised version after Thomas pointed out I have the very first calculation (and the easiest one), for the volume of the concrete block, incorrect. You you know why I need help.
Here goes again, can someone check the math on this.
I want to lift a concrete block from 15ft deep. (4.57m)
The block measures 60cm x 60cm x 30cm or 0.108 cubic meters. Equivalent to a displacement of 3.8 Cuft
It is estimated that the concrete has a weight of 150lb/cuft
3.8cuft x 150 = 570lb weight in air.(equivalent 259kg)
3.8cuft x 64lbs/cuft (upward force of sw) = 243.2lb (eqv 110kg)
In water weight of block = 570lb - 243.2lb = 326.8lb (148kg)
i.e. displacement to achieve neutral bouyancy is 326.8/64 = 5.1 cubic ft
Lift in tons 5.1/35 (35cuft req to lift 1 ton) = 0.15
say 0.16 tons of lift req for positive bouyancy
0.16 - 0.15 = 0.01 tons
0.01 x 2,240 (lbs in a ton) = 22.4lbs
22.4/64 (upward force) = 0.35 cuft lift capacity req
Considering aboulute pressure 15ft deep x 0.445 (increase per ft depth) + 14.7psi (atmospheric) =21.375 psi
21.375/14.7 = 1.454 ata
Vol of air req = 0.16 x 35 x 1.454 = 8.14 Cuft (0.23 cubic meters) of air required for successful lift.
Funny enough, 0.23 cubic meters is the exact volume of an empty 200ltr drum I have.
If I could call Archimedes or Boyle I would but you lot will have to do.
Any input appreciated.
Thanks.
hi! brain, pinky here.
ReplyDeleteyour on the right track, just a few schoolboy errors.
i assume that you intend to sink the drum while full of water then attach it to the block and fill it with air 15ft down using your scuba tanks.
an object whose density is equal to that of the fluid in which it is submerged will have neutral buoyany.
ok, superstar DJ's, here we go.
density = mass/volume
density(concrete) = 259kg/0.108 m^3 = 2398 kg/m^3
density(water) = 1000 kg/m^3
for this mass of concrete to achive neutral buoyancy
we require, density = mass/volume
1000 kg/m^3 = Mass of Concrete (259kg)/Volume(cf)
Volume(concrete needs to be to float)
Volume(cf)= 259/1000 = 0.259 m^3
Assuming this extra volume can be added at no extra weight gain which is valid as
density of air (at 1 atm), 1.22 kg/m^3 << density of water (1000kg/m^3), ( << means much much less )
Volume(cf) = 0.259 m^3 = volume(c) 0.108 m^3 + extra volume that's provided by the air
extra volume required is 0.151 m^3
with 200ltr = 0.2 m^3
so just stick your drum down and fill ere up boy,
she'll be right.
this next part is a bit redundant, but i include it so you can see where your answer came from.
but this volume needs to be filled up with air at 15 feet deep, where pressure = 1.45 atms
Boyle's Law states that the pressure of a given mass of gas, held at constant temperature, will vary inversely with the volume. This may be stated mathematically as:
P(1)V(1) = P(2)V(2)
where 2 donotes inital pressure or voulme and 1 denotes finial state
P(1) = Pressure at surface = 1 atms
V(1) = volume air would take at surface
P(2) = 1.45 atms (15 feet)
V(2) = 0.151 m^3
we have
V(1) = 0.22 m^3
so our volume of 0.151 m^3 of air at 15 feet will expand to
0.22 m^3 at the surface,
which is larger than the volume of the drum, but this doen't matter as at the surface or at 15 feet deep
the volume of air required to achive neutral buoyancy is still 0.151 m^3
due to water and concrete both being incompressible.