Hoover Dam Bridge 2
This is a continuation of the previous item.
A steady convoy of cement trucks are dumping cement into two
hoppers that feed two pumps. The pumps put the wet cement flow
into an 8 inch diameter pipe. The pipe runs almost straight
down 300 foot to the arch footing. The pumps run at 200 psi.
How much cement (in cubic yards) will be pumped into the reinforced
form in the 12 hour period from dusk to dawn?
A steady convoy of cement trucks are dumping cement into two
hoppers that feed two pumps. The pumps put the wet cement flow
into an 8 inch diameter pipe. The pipe runs almost straight
down 300 foot to the arch footing. The pumps run at 200 psi.
How much cement (in cubic yards) will be pumped into the reinforced
form in the 12 hour period from dusk to dawn?
Labels: mathschallenge
posted by Ragknot at
10:43 PM
10 Comments:
I would say the equivalent of 1 cubic mile of cement.
I suppose this can be worked out if you know the viscosity of the cement mixture, the friction of the pipe wall, and the formula for working it out.
that would be 1760 cubic yards of concreate so that would be approx. 176 trucks. that would be one dump every 4.09 min witch cant be done because it take approx. 5 1/2 min to empty it so if two where dumping at the same time it would take only 8 hours and add in just over 2 1/2 min so set up per truck and you got you 12 hours to pour 1 cubic mile. to add to this. this is figured out with standard 10yard dumps for a job that big they would of used pit trucks witch hold 19 yards so that could be done in about 7 hours
um............. 900000000000?
FIRST POST!!!!!!!!!!!!!!
First off the guy above me clearly doesn't know the meaning of the word first congratulations you should pick up a dictionary.
Second if you're still wondering about that 1mile^3 this its not gonna happen. Here is why.
1mile=5280ft =>
1mile^3=147197952000ft^3
8in diameter= 4in radius
(2)(3.141992654)(4in)^2=100.531in^2
(cross sectional area of the pipe)
Our last given is that the time allotted for the job is 12hours
Some conversion factors to use
1ft^2=144in^2
1mile=5280ft
Not lets convert the cross sectional are of the pipe into ft^2
100.531in^2(1ft^2/144in^2)= 0.6981219444444ft^2
So now lets assume all the cement is initially in the pipe (I know this isn't really the case but hypothetically speaking for calculations) The pipe is presumed to be cylindrical knowing the volume (1mile^3) and the area of the base (0.6981219444444ft^2) we can calculate the length of the pipe.
V=BH => H=V/B=(147197952000ft^3)/(0.6981219444444ft^2)=2108481660.51856ft
For ease lets convert that into miles.
(2108481660.51856ft)(1mile/5280ft)=39933424.5569mile
Now for the entire 1mile^3 to be put into place all the cement has to be pushed from one end to other, i.e. the entire length of the pipe. This also has to be done in 12hours so lets convert to mph
(39933424.5569mile)/(12hrs)=3327785.38mph
As you can see this is not even a reasonable speed for cement to travel through a pipe. So as for the original question goes no there is no way that 1mile^3 of cement could be poured in one night through one pipe.
To: Sinisterwolf89
That was a great post but we have already agreed that one cubic mile had to be a mistake. Someone made an error preparing the announcers story to go with the video.
Assuming that it was supposed to be one cubic ______ (something), what could it be? One cubic km... No. that's still unreasonable.
I have estimated that the true volume was from 1000 to 2000 cubic yards.
If for example, it was around 1760 cubic yards, then someone said thats about 1 mile. Then someone made the assumption that 1760 cubic yards equals one cubic mile.
(1760 yd * 5280 ft)
Of course, this is incorrect, but a novice might have made the error just trying to put the volume into more understandable terms for the TV show.
I do think that Ragknot makes alot of sense here seeing how 1mile=1760yards the person preparing the speech may have thought that 1760yard^3 was a 1mile^3 however that would be absolutely wrong. But to solve the The question presented here that are too many unknowns.
for all the ppl on hear trying to say you cant pour a cubic mile in a day are wrong we do that on a standard on some jobs. in fact we just poured 1.23 cubic miles for a bridge and all thoughs ppl using all though fancy calculations .....wow you got to stop over thinking things if its a cylinder use pie (3.19) and if its squared then h+w+l divided by 27 its very quite simple so dont say you cant till you actuly get your hands dirty and actuly do some real work
Are you preparing a dinner with a pie for desert? And what's your h+w+l / 27 ? Is it 3^3 to convert from ft to cubic yards?
Regardless, The question is what kind of a mistake this one is:
1) Possibly it was a mile long line of concrete trucks and the announcer thought he was funny saying it's a cubit mile of concrete.
2) I can see how someone who doesn't have a clue what a cubic mile is, might just say a mile long block of concrete with 1x1 yard or foot cross section is a cubic mile, but I doubt that's what happened
3) Most likely, the typo or announcer's carelessness was assuming there's only ONE 8 inch pipe ... I can't see how a huge construction like that would have been poured via a single pipe and only 8 inches in diameter... so there were probably many such pipes delivering concrete evenly to the entire base or to many reinforced areas in the entire volume of it...
Let's say there was in fact a cubic mile of concrete - how many such pipes would we need (someone above has already shown that the trucks are capable of unloading that much concrete in the 7-12 hour period so I'm not going to bother questioning that)
Also, someone has already calculated the speed needed to pump this much concrete through a single pipe so let's use that figure of 3327785.38mph
What would be a reasonable speed per pipe? Let's say 100mph then we'd need 33277 pipes ... this sounds like way too much although, if this was a million dollar pour than maybe the cost of reinforcement + pipes ... nah ...
If the pipes were 8 inches in radius not diameter - that'll give use 4x the ratio, still 8319 pipes, speed could go as high as what, 200mph? Maybe 500mps (unrealistic if not impossible), that's still 1663 pipes ... 300 ft long ... and who would pull these pipes up as the concrete fills up the construction? Or ... why use such a long pipe if the concrete could just be delivered to the edge and poured down dropping 300ft?
Now, if this single pipe was 8 feet in diameter then ... it's 16 times the diameter = 256 times the cross section so the speed of concrete would be 3327785 / 256 = 12999mph ... still way too much...
So what if they had a huge pipe, 8 YARDS in diameter ? That's 3*3 times slower = 1444mph - I don't think so...
My question is to Anonymous just before my answer ... how can you pour this much concrete in such a short time? What kind of a delivery system do you use? How many trucks have to be unloading simultaneously to get that much concrete in just 12 hours?
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