I don't have a graphic calculator. I only have MathCAD 9.0.0.0. Is there a way to graph the following steps in MathCAD...
...or to solve for f another way. This is just an example problem. Once I learn how to do it, I can use it on my homework problem. Here's the full context of the example problem...
Thanks,
Brent
ACCEPTED SOLUTION
Accepted Solutions
With worksheet I meant the Prime file which you posted.
I see no equation which would include the friction f, so obviously we can't derive it by any calculation.
But I see that the text mentions a "Moody diagram". I looked it up at Wikipedia and obviously its something you should have at hand in printed form (maybe as an appendix in a book). The curves in this diagram look like they are determined empirically. There is no function equation which would generate those curves. So neither a graphing calculator nor Mathcad can help with finding the friction number as both have no way to draw the lines we see in the Moody diagram. You have to use the printed copy you should have available and follow the instructions given.
First you lookup the value 56725.621. I used the diagram found at the German Wikipedia (the English Wikipedia shows diagram with epsilon/D and not D/epsilon as described in your text).
So first lookup the Reynolds number 56700 (56725.621) at the abscissa.
Go upwards until you meet the curve for D/epsilon = 8400. There is no such curve! There is one for 6000 and one for 10000. The one for 8400 has to be estimated somewhere in-between.
The you go to the left and read off the approximate value you have arrived at. Could be something like f=0.01475.
EDIT: WRONG!! I looked up 567000 at the abscissa but it should have been 56700. See my reply below.
The ...75 is overconfident megalomania. It is difficult to read accurately to ten thousandths. The value is certainly between the grid lines for 0.014 and 0.015 and obviously much closer to 0.015. You also should not forget that we are looking at log scales
So once again, neither a graphics calculator nor Mathcad can help here, since everything needed to determine f is only preprinted and not available in the form of equations or table values.
Of course, one could laboriously digitize the diagram and thus obtain a vast amount of table values. Mathcad could then use these for an interpolation function, which would make it easy to determine the corresponding friction factor for a given Reynolds number and a given D/epsilon ratio.
But someone would first have to undertake this laborious digitization of the diagram and then make the data available. 😉
With worksheet I meant the Prime file which you posted.
I see no equation which would include the friction f, so obviously we can't derive it by any calculation.
But I see that the text mentions a "Moody diagram". I looked it up at Wikipedia and obviously its something you should have at hand in printed form (maybe as an appendix in a book). The curves in this diagram look like they are determined empirically. There is no function equation which would generate those curves. So neither a graphing calculator nor Mathcad can help with finding the friction number as both have no way to draw the lines we see in the Moody diagram. You have to use the printed copy you should have available and follow the instructions given.
First you lookup the value 56725.621. I used the diagram found at the German Wikipedia (the English Wikipedia shows diagram with epsilon/D and not D/epsilon as described in your text).
So first lookup the Reynolds number 56700 (56725.621) at the abscissa.
Go upwards until you meet the curve for D/epsilon = 8400. There is no such curve! There is one for 6000 and one for 10000. The one for 8400 has to be estimated somewhere in-between.
The you go to the left and read off the approximate value you have arrived at. Could be something like f=0.01475.
EDIT: WRONG!! I looked up 567000 at the abscissa but it should have been 56700. See my reply below.
The ...75 is overconfident megalomania. It is difficult to read accurately to ten thousandths. The value is certainly between the grid lines for 0.014 and 0.015 and obviously much closer to 0.015. You also should not forget that we are looking at log scales
So once again, neither a graphics calculator nor Mathcad can help here, since everything needed to determine f is only preprinted and not available in the form of equations or table values.
Of course, one could laboriously digitize the diagram and thus obtain a vast amount of table values. Mathcad could then use these for an interpolation function, which would make it easy to determine the corresponding friction factor for a given Reynolds number and a given D/epsilon ratio.
But someone would first have to undertake this laborious digitization of the diagram and then make the data available. 😉
The Colebrook-White equation is a potential area for further development.
Here's one example, refining the value of the Darcy friction factor by using Mathcad's built-in function root to refine the graphical estimate.
Stuart
Am I doing something wrong?
EDIT:
Ahh! I am so far out of my comfort zone!
If you can see and read, you'll be ahead of the game!
First I noticed that the diagram from the German Wikipedia page which I linked to also provides the equation given by Stuart.
epsilon is called k in the picture and f is called lambda. Diameter is lower case d and Re is the Reynolds number.
I also noticed that there are three (actually four including the f=64/Re at the upper left) formulas, depending on ithe area we land with the Re and D/epsilon coordinates. I am not absolutely sure where the border lines exactly are and how we could tell from the input values alone which formula would apply. With the OP's value we seem to be in the "hydraulically smooth area"!?
But the main error I made was that I looked up the Reynolds number 567000 in the diagram and not, as I should have done, 56700. Embarrassing!
Using the correct position I come up with a value of approximately 0.0205 for f. If I now use the formula provided by Stuart (the gray one in the pic, the one with both summands) I get 0.02077 and if I use the formula for the smooth area (the red one) I get 0.02031. Both look reasonable.
Using the values from the script/book posted by the OP the formula for "smooth" is way off but the other two may both be suitable.
