minor engineering math problem

[Kali]

how many gallons in one mile of 1.25 inch pvc schedule 40 pipe? (Main problem: I don't know if 1.25 pvc is ID or OD, secondary problem is just the math - please show your work :P )

[SoCalDem]

1. pass

I musta-been-absent-that-day, teacher:rofl:

[hedgehog]

2. Try this site for the info you need:

http://flexpvc.com/WaterFlowBasedOnPipeSize.shtml

[Kali]

10. don't need flow rates or velocities (YIKES!)

just want volume

[hedgehog]

13. I noticed that after I posted, but if you look over to the right, there's

a bunch of links including this one:

http://flexpvc.com/PVCPipeSize.shtml

Have fun!

:hi:

[lumberjack_jeff]

3. 1 1/4" sch40 pvc pipe has an id of 1.360"

http://www.harvel.com/pipepvc-sch40-80-dim.asp

Pipe sizing is an odd thing. Originally, 2" standard wall pipe was 2" ID with a 3/16" wall thickness or 2.375" OD. Fittings were made to accommodate this OD. Steam boilers were designed to high pressures, so there was a need for stronger pipe, so they invented the system of schedules. "Standard wall" was incorporated as "Sch 40", Extra heavy was renamed "Sch 80" etc. But because all the fittings depended on a standardized outside diameter, nominal pipe sizes really have no relationship to any actual dimensional parameter.

1 1/4" pipe is 1.660 OD
1 1/2" pipe is 1.900 OD
2" pipe is 2.375 OD

The inside diameters vary depending on the schedule.

edited to look at the correct row.

[cloudbase]

7. And from there it's just

pi*r^2*h, where h is one mile. Convert to cubic inches and divide by the number of cubic inches per gallon.

[EOTE]

4. I can tell you that the 1.25" is almost definitely the outer diameter.

So you'd probably need to find out the ID or the thickness of the PVC to find out the answer to this problem. The area of a circle is pi*r*r, so if the internal diameter is 1", the area of the circle would be 3.14*.5*.5. Then you'd just need to multiply the area by the amount of inches in a mile to find out the volume in cubic inches. Then divide by the number of cubic inches in a gallon.

[EOTE]

9. And btw, there are 231.8 cubic inches in a gallon. FYI NT.

[Kali]

25. I didn't have a piece of it handy -

the scraps went off with the truck

[lumberjack_jeff]

33. OD = 1.660 n/t

[RC]

5. 1.25 is inside diameter.

Take a one foot section of 1.25 pvc.
Cap one end.
Fill with water.
Pour into measuring cup.
Take amount times 5280.
That is your answer.

1-1/4" 1.660 (~1-5/8", 42.164mm) 1.380 .140 370 180 80/250

http://flexpvc.com/PVCPipeSize.shtml

[Kali]

26. no, apparently that would be too logical

to have something actually measure out to what the freaking name of the thing is

more crap designed by men, I am sure - like automotive parts where every freaking bolt needs a different damn tool }(

[MadHound]

6. Figure out how many gallons are in one foot of that pipe,

Then multiply by 5,280(number of feet in a mile).

The formula would be V=πr2h where V is volume, r=radius and h is height. That is radius squared by the way. Once you have the figure for V multiply it by 5,280 feet.

[FreakinDJ]

8. ...

3.14 x (1.360"/2)2 x (5280' x 12")

x 0.0043 = gallons

4.55 x 63360 x .0043 = 1242.11 US gal

[Kali]

24. now you seem too high

I got something much closer to ptah's - around 400 gallons

but I am starting to glaze over now

[FreakinDJ]

27. my area of a circle is off

(Pi x R)squared is wrong

pi x R-squared

[Ptah]

11. 400.8 gallons/ mile

McMaster-Carr says ID of 1-1/4 pipe is 1.364"

http://www.mcmaster.com/#pvc-%28schedule-40%29-pipe/=ddh3f2
The area of a circle with a dia of 1.364 is 1.461 sq. inches.
There are 63360 inches in one mile.
The volume (in cubic inches) is 92583.54.

There are 231 cu. in. in a gallon.


92583.54/231 = 400.8

[Kali]

14. HA! thankyou!

I DID know the formula for volume of a cylinder, sheesh people!

and my guestimate of 5.3 plus or minus miles was 2000 gallons - not too bad eh?

(new pump is running 285 lbs pressure if you want to be impressed - we finally got a pressure gauge on it so we can better guess where a break in the line is:P )

[lumberjack_jeff]

19. Five miles of 1 1/4" pipe? With 300' of static head?

Yikes.

[FreakinDJ]

23. 129.8 psi

[lumberjack_jeff]

31. My calculator indicates that she should see about 100 psi at the house at 3gpm.

Surprising. I would think pressure drop would be greater.

[Kali]

35. I don't know what the pressure is up here but

we think we are getting a little over 6 gpm (took just under 9 seconds on my cell phone stop watch to fill a gallon pickle jar)

[FreakinDJ]

38. Oh please lets not go to flow calcs

I would have to break out my laptop and use the EA

I wrote a little Work Book for Instrument Techs a while back

Fluid Properties

Temperature
Pressure
Density and Fluid Expansion
Type of Flow
Inside Pipe Diameter
Viscosity
Reynolds Number and Velocity Profile
Hydraulic Phenomena

Pressure = ratio of Force over Area (P=F/A)
Density = ratio of Mass over Volume (p=m/V)
Specific Gravity = ratio of operating density to water (SG = P liquid / P water)

Fluid Expansion is -
V = Vo (1+B x (Delta Temp))
V = New Volume
Vo = Old Volume
B = Cubic coefficient of expansion
Delta Temp = temperature change

Boyle’s Law – The Volume of an Ideal Gas at constant Temperature varies inversely with Absolute Pressure V = K/P

Charle’s Law – The Volume of an Ideal Gas at constant Pressure varies directly with Absolute Temperature V = K x T

Ideal Gas Law – the combination Boyle’s and Charle’s Law
PV = n R T

[Kali]

34. that's only half way

it ultimatly goes a hair under 6 miles with 600 feet!

yeah


here is the baby that does it:

[lumberjack_jeff]

41. Impressive. Seriously.

Where's the pump suction? Directly underneath?

If you ever want to know the exact elevation difference between the house and the pump, with the pump off, record the PSI at the house and subtract that from the reading of the gauge in the photo. Multiply the result by 2.307 to get the elevation difference in feet.

[Kali]

43. this has been the problem this week

there is a standard 1.5 hp submersible in the well. The old green pump used to take water from both the well discharge and a storage tank above ground at the same time (a safety gimmick to prevent it running completely dry.) For some reason we can't quite figure out, (probably a slight change in the plumbing configuration) it won't work running both pumps at the same time, so this one is just getting water basically by gravity from a 6000 gallon storage that sits a few feet above it.

We originally had another submersible IN the storage tank but we burnt up three or four (under warranty) before somebody figured out the pressure fluctuations from the different places we were wanting to pump to, plus the too-frequent pipe breaks down low were causing the problem. And old well man set us up with the myers pump. It worked for 15+ years and will probably be rebuilt so we have second or a spare. If we had known the problems we were going to have with this new one the last week or so, we probably just would have went for the rebuild alone. As it was, the first one died before we had any rain and that well was the sole source of livestock water for an unknown time (turned out to be just a couple of days, but one can never know) So we were in a situation where a replacement was supposed to be the fastest solution. Ha!

[lumberjack_jeff]

55. Let me see if I understand.

The submersible (centrifugal) pump discharge has a tee in it. One leg goes to the 6000 gal storage, the other to the suction of the myers (positive displacement) pump.

Wouldn't the submersible pump run all the time? If nothing else, depending on the flow capacity of the myers pump, it could draw water through the centrifugal pump causing it to spin and destroying it quickly. Series pump installations are problematic. Series pump installations of different type pumps (centrifugal vs positive displacement) are almost impossible.

In a previous life, I spent 15 years designing pumps. I would divert the output of the centrifugal pump exclusively to the storage tank and equip it with a level switch to turn off the well pump when the tank is full (Depending on how tall the tank is, you might be able to do this with a pressure switch). I would set up the Myers to gravity feed exclusively from the tank. (It sounds as if this is how it's configured now) I would equip it with a pressure switch to shut off at about 280 psi and on at about 260. I would also put a large bladder tank near the house, or at some elevation high enough that it can handle the local pressure.

[Kali]

61. yes to the tee

yes the submersible would run "all the time" (manually turned on and off at the power box)

previously (from 15 years up until 10 days ago) it WAS in a series and it worked fine

additional ranch-rigged engineering for your amusement - the tee that goes to the storage goes up to top and then down inside to bottom as we never cut another opening down low - so discharge from that tank is with siphon (there is another tee and a valve off of that to fill a drinker (that had a float valve on it) but we hardly ever use it so the valve is shut and normally buried under 2 feet of sand (because the guy that originally started this project was working on the cheap too)

we are planning to add some timers and a float switch after we get a handle on the bill for this latest work (translation: been planning that for years and likely it still won't happen)

prior to the early 90's when this got started, the whole place survived off of stock ponds and 2 6-foot x 25-feet deep, concrete-cased, hand-dug wells (one, really) that used an old greasy pump jack run with an electric motor (REAL leather leathers in that cylinder LOL)

we would love to put in another shallow dug well but nobody seems willing or has a clue how to do it anymore and I sure as hell don't like handling shovels:scared: although I used to be the one that had climb down to fish out the drowned snakes and squirrels that occasionally found their way in.

[lumberjack_jeff]

76. No problem with a siphon, provided the pump is below the water level.

... and the pump can lift the water over the high point in the suction line and/or a foot valve is installed in the tank.

Assuming the pipe from the well to the tank and the suction from the tank to the Myers are separate pipes, and if you're okay with ranch/lumberjack engineering, consider a toilet bowl float valve in the tank to shut off the flow from the submersible pump. Install a normal pressure switch to shut off the submersible motor. Water level rises, float valve closes, pressure switch opens, pump shuts off.

Myers pump turns on, water level drops, valve opens, pressure at the submersible drops, switch closes, submersible pump turns on. Lather, rinse, repeat. Better than timers.

Do not climb into any pit where methane or hydrogen sulfide may be present. A hand dug well is an enclosed space.

http://www.cdc.gov/mmwr/preview/mmwrhtml/00001448.htm

I'm very familiar with the Michigan case. It was extremely tragic.

[Kali]

83. oh no - it is the same pipe

but we are planning to cut a lower hole for the myers pump as soon as we get caught up on the storages uphill and can leave that storage empty for a couple of days. (of course the dream was to use this system to run DOWNHILL by gravity from the streambed or the shallow wells up here. Yeah so then we went into a 20 year drought)

ooh good point about the hydrogen sulfide (forgot the abbreviation) the "upper" shallow well does get that nasty sulfer bacteria stench and coats things with black slime (and that is why it was only ever used for livestock) as do a couple of places that can get springy in wet years.

The old "lower" well that we used all my life was good water. Up pressure tanks for domestic use? heh, then we would have to replumb the house because I doubt the pipes could handle it. we have an old masonry tank with a roof and more or less screened off eaves that feeds the house by gravity.

I use a hose to fill the washer and a bucket for the dishwasher. I do NOT appreciate pressure-reducing automatic valves on appliances.:P

Someday we will modernize, but then the world may be out of electricity and we would be retro cool with our low tech gravity and solar composting drainages;)

[Gold Metal Flake]

22. The ranching stuff you do is interesting to me.

I wish I was closer to you. I'd visit and fix your old trucks for fun.

[Kali]

29. OMG, I would adopt you then!

we just beat the hell out of the dodge on this last pump "incident"

having to drive 3 or 4 miles just to go see if the water was making it half way, (then of course driving back when it wasn't) on these roads was painful

back and forth and back and forth and back and forth...

[wtmusic]

12. 228 gallons

3.14159 (pi) x r² (.2647) x 5280 x 12 = 52668 in³ = about 228 gallons

(with 1.029" id)

[Crabby Appleton]

15. Your value for pi is incorrect. nt

[wtmusic]

17. D'oh!

Thanks for correction. :blush:

[Kali]

16. that doesn't seem right

at between 6 and 7 gallons a minute it is taking 2 hours to go 3 miles (with a 300 foot climb, but that it too complicated for me) so I was guessing like 300 or so

[lumberjack_jeff]

18. 400 gallons

(3.1416(pi) * r2 (.4624))= 1.453 in^2 area

5280*12 = 63,360 inches per mile

92,000 cubic inches of water.

= about 400 gallons.

[FreakinDJ]

20. I got 1200 gal

[wtmusic]

21. That's correct

I was using earlier poster's i.d. of 1.029.

[lumberjack_jeff]

28. That was me. Sorry.

:blush:

[Speck Tater]

30. This is a microcosm of the political world!

Everybody seems to "know" something different, and yet everybody is completely sure of what they think they know. No two versions of "reality" agree.

If no two Democrats can agree about the diameter of a 1-1/4 inch pipe, then it's no wonder no two politicians can agree about ANYTHING.

[lumberjack_jeff]

32. There's only one right answer, and you can measure it with a ruler. n/t

[Speck Tater]

82. You'd certainly think so. But we still get half-a-dozen different claimed answers.

And that's my point. If we can't get consensus on something that has one, clear-cut, easy to verify answer, it's no wonder we never get consensus on other issues.

[Kali]

36. !!!

:rofl: :thumbsup:


seriously though, if you are inclusive of multiple viewpoints, give the conversation a little time and not jump to the first/easiest answers, a good approximation of reality emerges...

[TlalocW]

37. I don't quite understand this but here:

According to this site:
http://www.engineeringtoolbox.com/ansi-steel-pipes-d_305.html

A 1.25 inch pipe has an internal diameter of 1.38 inches so I assume it's something how 2 by 4's aren't actually 2 by 4s.

So the calculation would be

Pi * (1.38 in / 2)^2 * ( 5280 ft * 12 in / 1 ft ) * ( 1 gal / 231 in^3 )

TlalocW

[Kali]

39. at around 11 or 12 years of age I experienced my first great disillusionment of the world

when I worked for HOURS on the plans for something I was going to build with 1 inch lumber and then the reality of the ACTUAL dimensions RUINED EVERYTHING

[TlalocW]

40. In grad school

I got disillusioned with my department (applied mathematics - turned out the university didn't really have that program) and switched to electrical engineering (have an undergrad in physics). I took some undergrad classes to catch up, and for homework in one of them, the problem resulted in an impossible integral. I couldn't believe that homework at that level would do that, and I didn't think undergrad engineering students would know about numerical integration methods like Picard's, etc. so I went to ask the TA about it. She looked at the problem and said, "Make that variable 1." I looked at it, and it turned it into a simple integral so I asked her, "Why do we make that variable 1?" She replied, "We just do."

I quit grad school soon after and became a computer programmer. :)

TlalocW

[ProfessorGAC]

45. The ID is Bigger Than The OD?

That can't be right. I think it might be the other way around. That would make the wall thickness 0.065", or a little over 1/16th inch. That seems about right just thinking about how a piece of plastic pipe looks.
GAC

[Ptah]

51. PVC (Schedule 40) dimensions:

Inside Diameter 1.364"
Outside Diameter 1.66"

[ProfessorGAC]

59. Wow!

That's odd. That isn't even close to 1.25#. Probably the other schedules are the same ID. Just the OD changes. I don't even know if they make PVC in schedule 80. I know it's common in stainless steel.
GAC

[Kali]

62. yes they make schedule 80 pipe

but good luck finding fittings - they all seem to be 40

[pokerfan]

42. 398.447299

First I googled the spec for the I.D.: For 1-1/4" pipe, average I.D. is 1.360 in. (http://www.harvel.com/tech-specs-pvc-pipe-40.asp)

Then some google math because I is lazy engineer:



You have to double check the syntax to make sure it understood you correctly but it's pretty awesome. We could have avoided the Mars Climate Orbiter disaster in 1999 had NASA had this technology. :)

[Kali]

46. and I do appreciate the 6-decimal point figure

:rofl:

we used to have a Soil Conservationist (now Natural Resources Conservation Service) who obviously had a good engineering background.

We would get these plans for stuff with figures to 4 decimal points. Then we would go sink a railroad tie to however deep we could dig and tie it up with baling wire.

or like when we originally did this pipeline project - specs were anytime pipe was above ground it had to be steel - so one place where we went through a culvert under a road we dutifully used steel. That place is the FIRST one we look when there is a break in the line, because the steel to pvc joint breaks so often.

If it had been all plastic it probably would have got a little sunburnt for a couple feet but would still be holding...:eyes:

[pokerfan]

57. Yeah, I threw that in for the giggles

But that answer is correct assuming the average I.D. specification is correct.

Area of the cross-section: pi * r^2 = Pi * (1.36/2)^2 = 1.45 in^2
Length in inches: 5280 ft * 12 in/ft = 63360 in.
Volume = Area * Length = 1.45 in^2 * 63360 in. = 91872 in^3
1 US gallon = 231 cubic inches
91872 / 231 = 398 gallons

And all this reminds me of my favorite engineering joke:

A mathematician, a physicist and an engineer were all given a red rubber ball and told to find the volume.

The mathematician carefully measured the diameter and evaluated a triple integral.

The physicist filled a beaker with water, put the ball in the water, and measured the total displacement.

The engineer looked up the model number in his Red-Rubber-Ball table.

[TlalocW]

69. At my undergrad, the math professors used to say this

Sociologists think they're psychologists
Psychologists think they're biologists
Biologists think they're chemists
Chemists think they're physicists
Physicists think they're mathematicians
Mathematicians think they're gods (they're right)

TlalocW

[pokerfan]

72. xkcd 435

[lumberjack_jeff]

47. but it still fails 48÷2(9+3)

:)

[pokerfan]

54. Yeah

Frustrating that it chokes on something so straightforward. Like I said, you really have to double-check. But it's handy for unit conversions:

[lumberjack_jeff]

56. that's awesome, I need to use that more often. n/t

[ProfessorGAC]

44. Assuming ID

5280 feet in a mile. Diameter is 1.25/12 feet, so radius is 1.25/24. (1.25/24)^2 times pi * 5280 gives cubic feet.

7.5 gallons in a cubic foot.

Sorry, i don't give answers. Only instructions on how to get the answers.
GAC

[Ptah]

48. ?

1.25/24 = .052

.052^2 = .0027

.0027*pi = .0085

.0085 * 5280 = 44.99

44.499 / 7.5 = 5.99 Gallons

:wtf:

[ProfessorGAC]

49. Um! I Said 7.5 Gallons In A Cubic Foot

If you have cubic feet you MULTIPLY the cubic feet by 7.5. You divided it. That makes your result off by a factor of the square of 7.5.
GAC

[Ptah]

52. My mistake.

44.499 * 7.5 = 333.7


:blush:

[EOTE]

50. You divided when you should have multiplied.

7.5 gallons in a cubic foot. If there are 44.5 cubic feet, you need to multiply that by 7.5 to get the total number of gallons.

[Ptah]

53. oops

44.499 * 7.5 = 333.7

:blush:

[pokerfan]

60. This is what crashes Mars probes!

[ProfessorGAC]

63. And Makes The Hubble Blurry

Another "oops".
GAC

[Kali]

66. wait! wut?

so my original guess of 300 was even closer than I thought? hahahahhahahahhaha:woohoo:

oh wait again - that was for if the ID was actually 1.25?

[ProfessorGAC]

71. Yeah

Somebody posted the actual ID. It was a lot bigger than 1.2". So, the number would be higher than my solution would provide. Same math, just a different ID.
GAC

[HappyMe]

58. What time does the train leave New York?

:silly:

[pokerfan]

64. xkcd 356

[lumberjack_jeff]

77. LOL! n/t

[ProfessorGAC]

65. Stardate 11522.7

Now, are you happy you're so funny?!?!?
GAC

[HappyMe]

67. I wasn't making fun of anyone or anything!

I admire people that can do super complex mathematical equations.


I apologize if anyone was offended, and will take my misguided humor elsewhere.

[ProfessorGAC]

70. I Was Only Kdding Back

No, i'm sorry if i came off wrong. I actually thought your post was funny.
GAC

[pokerfan]

74. Here's a fun one

Burt works in the city and lives in the suburbs with Ernie. Every afternoon, Burt gets on a train which arrives at the suburban station at exactly 5pm. Ernie leaves the house and drives so as to arrive at the station at exactly 5pm to pick up Burt. The route that Ernie drives never changes and his driving speed is constant.

One day Burt gets to leave early and catches an earlier train arriving at the suburban station at 4pm instead of 5. Instead of calling Ernie to ask for an earlier pick-up, Burt decides to get some exercise and begins walking home along the route that Ernie drives knowing that eventually he will meet Ernie and they will ride home together in the car.

This is what happens and Burt ends up arriving at home ten minutes earlier than normal. Assuming that Burt's walking speed is constant and no time is lost on the pick-up, for how many minutes does Burt walk?

[Gregorian]

68. It depends upon whether it's schedule 40 or schedule 80

http://www.engineeringtoolbox.com/pvc-cpvc-pipes-dimensions-d_795.html

Otherwise, I'm sure the process of calculating volume has been done in the replies above. Very basic stuff. 8th grade math.


Whoops, lumberjack jeff already mentioned this. Bravo.

[Permanut]

73. Okay, or you can do it the easy way

and just pray for the answer. I got 7.2, but I'm not sure if that's in hins or logs.

[Yavin4]

75. I Was Told That There Wouldn't Be Any Math on DU

I would like a refund.

[pokerfan]

78. LOL

OK, President Ford...

[lumberjack_jeff]

79. Do you mean PVC or Poly pipe? Did you buy it on a rolll?

Given the pressures you're using, I suspect you did mean PVC.

[Kali]

81. yes PVC

and of COURSE, I wasn't involved in gluing the god knows how many joints in the lower half of this (yes I know, 3 miles divided by 20 feet) so for many of the past ten years we have been replacing EVERY SINGLE JOINT in the lower, higher pressure 2 miles or so. Because if there is one thing I know how to do it is glue pipe! (I did the upper 2.5 miles before we did switch over to poly for a run over solid rock above ground)

[JBoy]

80. Tag this with "Threads you won't see on FR".

LOL.