Question 505 - WR NCEES Sample Questions

[owillis28]

First of all, I would like to thank everyone who has answered my posts (there have been many). I appreciate the help. I find it is better to post the question that you look for the answer and waste 2 hours.

On to the question...............

In the problem number stated above, the use a form of the Hazen-Williams equation to solve for the total dynamic head for the pump.

The equation is Q = V*A = 1.318 C A R0.63*S0.54

Can anyone tell me where this equation came from? Is it an equation from the CERM manual that has been "adjusted" to solve for 'Q'? I tried selecting the correct equation from the CERM manual using the definitions and my knowledge on how I would solve the problem.

I have not been able to understand and obtain the correct answer for this problem.

Please Help!

P.S. If anyone has any problems with written out solutions in PDF format, I would love to have a copy. I want to do a lot of these types of problems because I haven't seen these since college.

 

[Guest]

owillis28--

The Hazen-Williams Equation that you presented is an emperical equation for determining head losses or pressure drops in a closed conduit. So, in other words, the equation is derived in the same manner that the Manning Equation was developed .... fitting a curve to observed points.

In terms of the term 'correction,' they are most likely referring to the 'C' value which functions in the same way that 'n' functions in the Manning Equation - it is a correction (linear multiplier) to the equation that is a function of Area (A), Hydraulic Radius ( R ), and Slope (S).

Hope this sheds a little light on the subject.

JR

 

[owillis28]

owillis28--
The Hazen-Williams Equation that you presented is an emperical equation for determining head losses or pressure drops in a closed conduit. So, in other words, the equation is derived in the same manner that the Manning Equation was developed .... fitting a curve to observed points.

In terms of the term 'correction,' they are most likely referring to the 'C' value which functions in the same way that 'n' functions in the Manning Equation - it is a correction (linear multiplier) to the equation that is a function of Area (A), Hydraulic Radius ( R ), and Slope (S).

Hope this sheds a little light on the subject.

JR

Should this equation be used in EVERY problem where you need to calculate total dynamic head to obtain the system head curve (TDH)? Is this equation, or some form of it, referenced in the cerm manual?

Thanks for your help.

owillis

 

[Cheese]

The Hazen-Williams equations are in the CERM. In several places (including on the same page as the Darcy head loss equations).

The H-W equation is far easier to use when solving for system curves (plotted vs pump curve) because you are evaluating at multiple flow rates. Using the H-W equation, the 'friction factor' does not change for various flow rates. Trying to evaluate using Darcy would be very cumbersome as the 'f' value would change for every flow rate (velocity changes).

The H-W equation is pretty good for "standard, clear, cold, drinking water" in 'drinking water pipes' at 'drinking water flow rates'. The equation breaks down all over the place while the darcy equations are good for all flow types and rates, etc and are thus generally used more frequently (although it is much harder to use).

Be careful when picking the correct form of the H-W equation, as the units are VERY important (ft3 vs gal, or inch vs feet in diameter, etc).

H-W and Darcy equations calculate head loss due to friction. This step is just a part in solving for flow rate which uses the contunity and momentum (bernuli) equations.

Hope this helps,

Cheese

 

[owillis28]

Cheese,

Do you have a solution to this problem using H-W equations from the CERM? Would you be willing to post your solution(s)?

I do not come up with the same answer and have gone through my calcs a couple different times.

owillis

 

[Cheese]

owillis,

try solving with equation 17.31 page 17-7 in CERM 10.

head loss = 10.44*L*Q^1.85 / C^1.85*d^4.87

d is in inches

q is in gpm

L= feet

the two H-W equations on this page are the ones I use.

Solve this for several flow rates (gpm = 400,600,800,1000). Add this head loss to the elevation head, ignore velocity head (long lenghts of pipe) and you have your system head required.

If this doesn't work, I can solve on paper, scan and send tomorrow.

Cheese

 

[civilsid]

One comment on friction factor "f"- I know all about doing those iterative questions and they take way to much time. In general, it is easier and more accurate to use the appendix than it is to read it off the Moody diagram like I used to do. Also, you can scan down the "f" values and I pick one that is where the curve flattens out- you will see the same f for about half a dozen different Re values. This usually gets you "close enough for government work". :joke: