Equivalent Length of Pipe

[ktulu]

I am working through a problem where I need to find the equivalent length of concrete pipe. The CERM only gives equivalent length values for steel and cast iron.

Where would I find a quick list of equivalent lengths for generic fittings for materials other than steel and cast iron?

TIA.

ktulu

FYI: the solution gives an equivalent length of 125 for a check valve, 11 for a gate valve, and 31 for a long sweeping elbow.

 

[IlPadrino]

Can you post the problem?



where:

k = coefficient

D = diameter of pipe (ft)

f = friction factor

There are lots of ways to find the friction factor... I assume that's not the problem.

The loss coefficients are listed at PE Notes - Hydraulics under the Equivalent Length, Circular Pipes section.

I think I've seen tables for non-steel equivalent length, too... let me take a look.

 

[IlPadrino]

Now you've got me thinking...



The manning coefficient for smooth steel is something like 0.012 and for concrete is something like 0.013... Not a huge difference. What's wrong with using the equivalent length of steel pipe tables for fittings and adjusting by a factor of 1.17 (0.0132/0.0122)?

 

[MGX]

Now you've got me thinking...
View attachment 1624

The manning coefficient for smooth steel is something like 0.012 and for concrete is something like 0.013... Not a huge difference. What's wrong with using the equivalent length of steel pipe tables for fittings and adjusting by a factor of 1.17 (0.0132/0.0122)?

Could you use the hazen-williams equation using C=100 or so? I've only cement asbestos C factors handy.

I could help more if I knew the ID of the pipe in question.

 

[ktulu]

Here is the problem:

Water is pumped from a reservoir at elevation 100.0 feet to a second reservoir at elevation 150.0 feet through an 18 inch diameter line at a flow rate of 9 MGD. The pipeline is concrete and has a roughness coefficient of f = 0.018. The water is transferred a distance of one mile and contains: one check valve, two gate valves (open), and three long-sweeping elbows. Assuming a pumping efficiency of 80%, what is the monthly power bill if electricity costs $0.10/kW-hr?

I found a table in Chelapati Section 12 that has approximate equivalent lengths.

 

[IlPadrino]

where:

HP = work done by the pump (hp)

γ = specific weight of the fluid (lb/ft3) = 62.4 lb/ft3 for water

hp = head of pump (ft)

Q = discharge (ft3/sec)

So the only difficult question here is the pump head. Using the Energy Equation...



where:

P/γ = pressue head (ft)

v2/2g = kinetic head (ft)

Z = potential head (ft)

hp = head of the pump (ft)

hL = head loss (ft)

So hp is simply Z2-Z1 + hL, or 50ft + hL. Given the length of the line (5280ft), I'd think you can ignore the minor losses and still get an answer that's close enough. So first worry about the friction loss of the water just due to the mile of pipeline. I have a nomograph and a table that gives loss in feet per 100 feet length of pipe assuming C=100. Given C for concrete pipe is around 130, it requires the flow of 6250 gpm to be scaled by 130/100 (i.e. 4808 gpm). For 18" pipe this is somewhere around 1.3 ft/100 ft of pipe... or 65 ft for a mile.

Frankly, I'd stop there and calculate HP for 115 feet of pump head... but if you wanted to be exact, my other comments still stand.

So... what's the answer?

 

[snickerd3]

Here is the problem:
Water is pumped from a reservoir at elevation 100.0 feet to a second reservoir at elevation 150.0 feet through an 18 inch diameter line at a flow rate of 9 MGD. The pipeline is concrete and has a roughness coefficient of f = 0.018. The water is transferred a distance of one mile and contains: one check valve, two gate valves (open), and three long-sweeping elbows. Assuming a pumping efficiency of 80%, what is the monthly power bill if electricity costs $0.10/kW-hr?

I found a table in Chelapati Section 12 that has approximate equivalent lengths.

They have those kinds of questions on the Chem E test too. I spent a LOT of my studying on this topic...not that I remember how to do them now. Feels like the whole morning part of the Chem E exam I took was problems very similar with a slight twist.

 

[IlPadrino]

Could you use the hazen-williams equation using C=100 or so? I've only cement asbestos C factors handy.
I could help more if I knew the ID of the pipe in question.

where:

hf = friction head loss (ft)

L = length of pipe (ft)

Q = discharge (ft3/sec)

C = Hazen-Williams Coefficient

D = diameter of pipe (ft)

Sure... that would work for calculating the head loss but the original question remains: what's the equivalent length of the minor losses? And C for concrete is 120-140 (I show asbestos cement as 140).

One has to decide if they like formulas or prefer tables/nomographs to answer problems like these.

 

[ktulu]

I agree with your reasoning, IlPadrino, except that 50 + 65 = 115 feet. The solution that I have actually used the velocity head, which was determined to be a mere foot of head. So I agree with you - that it could be disregarded to save time during the exam.

 

[IlPadrino]

I agree with your reasoning, IlPadrino, except that 50 + 65 = 115 feet. The solution that I have actually used the velocity head, which was determined to be a mere foot of head. So I agree with you - that it could be disregarded to save time during the exam.

Those are the silly mistakes that might haunt you if you fail by a question or two, huh?!?

Velocity head and equivalent length methods for determining minor losses are similar in that they are related by the equation:



The hardest part of this question would have been in dealing with the friction factor, f. In the problem statement "f" is called "roughness coefficient", which when I had first read it I thought was the manning coefficient, n. Odd, though, because f is a function of relative roughness and the Reynolds number. Does their solution verify it is really the friction factor "f" and not "n"?

 

[ktulu]

It is the friction factor, b/c they use the Darcy equation to find head loss due to friction.

And yes, those silly mistakes definitely can cause heartache. They have haunted me, for sure.

 

[IlPadrino]

It is the friction factor, b/c they use the Darcy equation to find head loss due to friction.
And yes, those silly mistakes definitely can cause heartache. They have haunted me, for sure.

Yeah, if you use the Darcy-Weisbach Equation



where:

hf = friction head loss (ft)

f = friction factor

L = length of pipe (ft)

D = diameter of pipe (ft)

V = velocity (ft/sec)

then this is a quick minute to get the pump head - all you've got to do is convert the flow to velocity and then plug away. I've never heard of "f" called the roughness coefficient, though... anyone else?

 

[IlPadrino]

Oh.. and PE Notes - Water Resources Problems has only one problem, but it's very similar and I think is very useful in laying out the different approaches to solving a problem. Notice how much quicker you get an answer when you use the tables instead of equation!

 

[Water_PE]

Here is the problem:
Water is pumped from a reservoir at elevation 100.0 feet to a second reservoir at elevation 150.0 feet through an 18 inch diameter line at a flow rate of 9 MGD. The pipeline is concrete and has a roughness coefficient of f = 0.018. The water is transferred a distance of one mile and contains: one check valve, two gate valves (open), and three long-sweeping elbows. Assuming a pumping efficiency of 80%, what is the monthly power bill if electricity costs $0.10/kW-hr?

I found a table in Chelapati Section 12 that has approximate equivalent lengths.

hey Ktulu,

You are doing a wonderful help for the other people taking PE exam. I really appreciate. I hope you post some more questions everyday or atleast whenever you got time.

Continue with yuor good work!!!!

 

[pinkpig]

I am working through a problem where I need to find the equivalent length of concrete pipe. The CERM only gives equivalent length values for steel and cast iron.
Where would I find a quick list of equivalent lengths for generic fittings for materials other than steel and cast iron?

TIA.

ktulu

FYI: the solution gives an equivalent length of 125 for a check valve, 11 for a gate valve, and 31 for a long sweeping elbow.

Can you just use minor loss coeff instead of equivalent length? Minor loss=(K1+K2+...)V^2/2/g. Or ignore minor loss at all. Pick up an answer which is close to but bigger than what you get(since you ignore minor loss, the calculated pump head h will be less than the actual value).

 

[pinkpig]

Now you've got me thinking...
View attachment 1624

The manning coefficient for smooth steel is something like 0.012 and for concrete is something like 0.013... Not a huge difference. What's wrong with using the equivalent length of steel pipe tables for fittings and adjusting by a factor of 1.17 (0.0132/0.0122)?

The equation above is in fact Manning's equation for a pipe with D, L, n. (s=hf/L in manning's equation, s is only equal to channel bed slope S0 under uniform flow).

My question is: can we use Manning's equation for a pressurized flow?

 

[IlPadrino]

The equation above is in fact Manning's equation for a pipe with D, L, n. (s=hf/L in manning's equation, s is only equal to channel bed slope S0 under uniform flow).
My question is: can we use Manning's equation for a pressurized flow?

While Manning's is usually used for open channel flow and Darcy-Weisbach and Hazen-Williams used for fluid flow in full pipe (i.e. pressurized), you can use Manning's equation for friction head in pressurized pipes. I'm sure the 100-lb brain PhDs could explain why Manning's is not the preferred method given one of the others...

For the exam, I wouldn't worry too much... if they give you C, use Hazen-Williams... if they give you n, use Manning... and if they give you f, use Darcy-Weisbach.

In this problem, they gave you f (even though they used a strange name for it), so it was an obvious choice. I wouldn't assume an f if it's not give... but you could easily assume an n or a C. So how do these two equations compare given the rest of the problem? I don't have a calculator handy, but give it try and let us know.