Critical Depth in Circular Pipe

Forum|Forum|15 years ago
February 11, 2011
5 replies
10334 views

I have attempted to derived the symbolic equation for critical depth for a circular pipe. Assuming that formula that I have derived is correct (others may be able to shed some light here because I could not find a published formula on the web or in the text books that I have for that purpose) I then tried to calculate numerical values of critical depth based on an assumed flow increments (input vector of Q-values). To do this I have used a solve block but for some reason however it doesn't result in an answer i.e. vector of critical depth values. I did however find an empirical formula for Critical Depth in Circular Pipe which gives a result which I have graphed. I am aware however that the empirical formula is applicable only over a certain range of flow. My aim however is to compare that empirical formula to the exact value. Can someone help me figure out why the solve bock fails to produce an answer? Maybe the derivation is incorrect?

Thanking you in advance.

Kind regards, Mark Buckton

1_CriticalDepth-xmcd.zip

Other

Best answer by AlanStevens

How about as in attached?

Alan

P

PhilipOakley

1-Visitor

Mark,

I googled "Critical Depth in Circular Pipe" to get a number of good hits with theory, it may be that I got lucky with a good search phrase

http://www.lmnoeng.com/Channels/CriticalDepth.htm

http://www.lmnoeng.com/Channels/gvf.htm

http://www.alanasmith.com/theory-Pipe-Design.htm

Philip

M

MBuck2

Author

1-Visitor

Yes I saw these also but the form of the equations appear to be very different from each other therefore which one is correct? Also both pages just state an equation but don't derive it from first principles. The general formula is 1-Q^2*T/(g*A^3)=0 but that expression must take the channel geometry into account i.e. an expression for top width and flow area in a pipe. I believe I have done that but the real question is why MathCad 15 cannot form a solution?

Regards, Mark