CE Six Minute Problems Water and Environmental Resources

[brindiz]

Hello,

For all of you out there will you please help me understand how the friction factor was derived for this problem. When I calculate it from the number that they have on the equation I get 0.0240, and they list 0.0419??

Any help will be greatly appreciated.

 

[IlPadrino]

Post the problem and I'd gladly explain.

 

[brindiz]

Post the problem and I'd gladly explain.

Water is pumped from an elevation of 3457 ft to an elevation of 3503 ft through 500 ft of 2 in schedule-80 steel pipe at a velocityof 5 ft/sec. The pipe includes 15 couples, eight 90 degree regular elbows, four 45 degree regular elbows, six tees (straight flow), and two globe valves. All fittings are standard pipe thread. The water temperature is 60 degrees F. What is the total head loss in the pipe from all the sources?

Answers are:

A) 24 ft

B) 74 ft

C) 86 ft

D) 270 ft

Need to get the equivalent length from all the fittings this is equal to 239.75 ft.

The inside diameter for 2 in schedule-80 steel pipe is 1.939 in. and epsilon is equal to 0.0002ft

Need to calculate Reynold's number and kinematic viscosity for water at 60 degrees F should be 1.217 x 10 exp -5

Problem uses swamee-jain equation to solve for friction.

f=0.25

-----

[log10(epsilon/D/3.7 + 5.74/Re^0.90)]^2

Total head

hf = f(L+Le)v^2

-------------------

2Dg

g = 32.2 ft/sec^2

The solutions at the back of the book state the answer for f is equal to 0.0419, when I calculate the equation I get 0.0240, yielding a total head loss of 42ft. The answer should be 74 ft.

I have used the Moody diagram and I am calculating around .0240 value.

Please help and thanks in advance.

 

[IlPadrino]

The solutions at the back of the book state the answer for f is equal to 0.0419, when I calculate the equation I get 0.0240, yielding a total head loss of 42ft. The answer should be 74 ft.I have used the Moody diagram and I am calculating around .0240 value.

Please help and thanks in advance.

OK... I'll take a look when I get home. In the meantime, check out the thread http://engineerboards.com/index.php?showtopic=3890 as I think it's a good discussion on how to solve a similar problem in less than six minutes.

 

[IlPadrino]

OK... something isn't working for me...

I agree with your equivalent length of the fittings (240ft) so Leq=500+240=740ft.

I agree with your calculation of f (0.02385) and I also get similar numbers using various Moody diagrams (my favorite is one that uses VD" along the top for water at 60F for steel or wrought iron - it avoids the need to calculate Re, and it has diameter along the right which is convenient when you stop worrying about schedule).

I agree with your Darcy-Weisbach equation for hf (about 41ft).

The problem I have is if I use Hazen-Williams (you just need to come up with a value for C), I get about 71ft... I've never come up with such a radical difference between the two! I wish it was a problem with f, but the fact that I get the same answer using equations, charts, and tables makes me doubt that.

So I'm stumped...

Also, if the problem is asking for total headloss in the pipe, you've got to add the loss due to the change in elevation (46ft).

Can you please post the actual (scanned) problem and solution?

Oh... and I wouldn't worry about using actual inner diameters for the exam - the added precision isn't going to change the answer enough to get even close to a different choice.

 

[MEPE2B]

Since the problem uses standard 2" sch 80 steel pipe with standard water, with no special roughness factor to consider, and no special viscosity to consider, I would approach this problem using short cuts to save time. I pull out my trusty Cameron Hydraulic Data book, 19th ed. (which is an invaluable tool for making quick work of problems like this).

I turn to the table for friction of water in new steel pipe (based on Darcy's Formula), and on page 3-16 I find 2 inch pipe, sch 80 and follow the velocity row down to where 5 ft/sec would fall. I do a quck interpolation between listed velocities of 5.43 and 4.89 to get a head loss per 100 ft of 5.496 ft when the velocity is 5 ft/sec. I also see in this table that the ID of the pipe is 1.939"

Next I need equivalent lengths for the fitting and valves, so I turn to the section for Friction of Water Head Losses Through Valves and Fittings, starting on page 3-110, where L/D and K are tabulated for various fittings and valves. Cameron takes this info from Crane Technical paper no. 410, and is based on Darcy. It's a quick task to find the following L/Ds:

90 deg ell: L/D=30

45 deg ell: L/D=16

thru tee: L/D=20

globe valve: L/D=340

there is no listing for couplings, but it is common practice to assume a 45 deg ell to be an equivalant loss to a coupling

Multiply the quantity of each type of fitting times each L/D, then times the ID and sum up to get the total equivalent length for fittings, Lf:

Lf = [8(30)+4(16)+6(20)+2(340)+15(20)]x(1.938/12) = 226.7 ft.

Total equivalent pipe length = 500+226.7 = 726.7

Head loss due to pipe and fitting friction is Hf = (726.7/100)x(5.496) = 39.94 ft.

Head loss due to elevation change is He = 3503-3457 = 46 ft.

Total head loss HL = 39.94+46 = 85.94 ft.

I would choose answer © 86 ft.

Since we are all getting a similar answer ( I think we would have all chosen choice C), I suspect an error in the answer/solution shown in the book.

 

[IlPadrino]

Since we are all getting a similar answer ( I think we would have all chosen choice C), I suspect an error in the answer/solution shown in the book.

What about if you use Hazen-Williams to come up with hf?

 

[MEPE2B]

What about if you use Hazen-Williams to come up with hf?

I have the following as the Hazen and Williams empirical formula:

hf=[0.002083L(100/C)^1.85]x[(gpm^1.85)/(d^4.8655)

where L is equivalent pipe length in feet, d is pipe ID in inches, gpm is flow in gallons/minute

from velocity = 5 ft./sec., d=1.939 in., then gpm = 46

We had L=727

So, hf=[0.002083(727)(100/C)^1.85]x[(46^1.85)/(1.939^4.8655)]

hf=71.96(100/C)^1.85

Therefore, the answer depnds on what you choose for C

From Cameron, I read C for welded or seamless steel pipe to be within a range of 150 to 80, with 130 as the average value for clean, new pipe

Using C=130, hf=44.6

Using C=100, hf=71.96

Using C=80, hf=107.9

Using C=150, hf=33.8

To match the Darcy calculation where hf= 40 ft, we'd have to choose C=136.9, which is in the range given

However, not having the luxury of working backwords, I would have chosen the average C=130, giving hf=44.6, and hl = 44.6+46=90.6 ft. , and I still would have chosen answer C. 86 ft. ( the closest choice)

 

[IlPadrino]

To match the Darcy calculation where hf= 40 ft, we'd have to choose C=136.9, which is in the range given
However, not having the luxury of working backwords, I would have chosen the average C=130, giving hf=44.6, and hl = 44.6+46=90.6 ft. , and I still would have chosen answer C. 86 ft. ( the closest choice)

Yeah... the answer is pretty sensitive to what value you choose for C. The CERM (App. 17.A) says it's range is 150-80, clean is 140, and design is 100. Then there are notes at the bottom that say new should use 130, 5-year-old should use 120, 10-year-old should use 105, etc. I guess given the uncertainty here it's hard to choose. Or would you suggest you might always go with the "clean" values?

I'd forgotten about Crane... what an awesome publication that can give you some really good shortcuts. For example, there's a table that gives you pressure drop for sched 40 steel pipe - all you need to know is velocity or discharge and diameter. If you want to get more exact, it provides a correction factor for other than sched 40 (simply multiply the square of the ratio of the d40 to dact). It would make VERY quick work of this problem.

 

[MEPE2B]

Yeah... the answer is pretty sensitive to what value you choose for C. The CERM (App. 17.A) says it's range is 150-80, clean is 140, and design is 100. Then there are notes at the bottom that say new should use 130, 5-year-old should use 120, 10-year-old should use 105, etc. I guess given the uncertainty here it's hard to choose. Or would you suggest you might always go with the "clean" values?
I'd forgotten about Crane... what an awesome publication that can give you some really good shortcuts. For example, there's a table that gives you pressure drop for sched 40 steel pipe - all you need to know is velocity or discharge and diameter. If you want to get more exact, it provides a correction factor for other than sched 40 (simply multiply the square of the ratio of the d40 to dact). It would make VERY quick work of this problem.

Yeah, it seems very sensitive to C. I guess for exam purposes, I would assume new or clean pipe, unless the problem states otherwise. If I was doing a calculation for real life design purposes, I would probably choose a more conservative number to allow for some scaling or fouling to occur in the pipe as time goes on. Selecting C=100, and then adding 10% to the developed head would probably provide a reasonable margin for a pump selection in real life.

To me, both Crane and Cameron are indespensible in everyday practice. And I found them very useful in the PE exam. I don't know about the Civil or Environmental exams overall, but for the Mechanical exam, having these two books and being familiar with them will give you a leg up.

See the attached pages referenced from Cameron. Anybody interested in purchasing a Cameron book can get it from Flowserve at the following web page:

https://www55.ssldomain.com/fpdlit/Merchant2/merchant.mvc?