Is the weir coefficient really unitless?
Doug Trieste
I was wondering if someone can provide me with a logical answer to the following associated with weir coefficients? Here is my problem.
- The weir equation is Q = Cw x L x H^1.5, where Q is flow over a weir in cubic feet per second, Cw is suppose to be unitless, L is in feet, and H is in feet (of course SI units are also applicable).
- Taking the units associated with L x H^1.5, we get (feet) x (feet)^1.5 = (feet)^2.5
- If Q has the units of cubic feet per second, doesn't this indicate that Cw is NOT unitless? Instead, it appears that there are units associated with Cw, which are (feet)^0.5 per second. Otherwise, it is not feasible to get Q in cubic feet per second.
I, like many others in the profession, have always assumed
that Cw is unitless. However, I am wondering if there really are
units associated with Cw.
Any comments and supporting documentation will be greatly appreciated.
Thanks
Jerald S. Fifield, Ph.D., CPESC, CISEC
HydroDynamics Incorporated
P.O. Box
1327
Parker, CO
80134
Phone: 303-841-0377
Fax: 303-841-6386
E-Mail: h...@ecentral.com
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Chandan Das
Jerald,
You are right. Cw is not unitless but has a coefficient of ft^0.5/sec. For a trapezoidal weir (Cipoletti weir) for example Cw is approximately equal to 1.86 in SI units and 3.367 in U.S. units. I normally use the CRM (Civil Engineering Reference Manual) by Lindeburg (Eleventh Edition). See Page 19-13. Hope that helps.
Regards,
Chandan Das, Ph.D., P.E.
Water Resource Manager
J.F.Sato & Associates
5878 South Rapp Street
Littleton, Colorado 80120
Tel: 303.797.1200
Fax: 303.797.1187
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Bill Ruzzo
You probably can also find your answer in King & Brater “Handbook of Hydraulics” (McGraw Hill 1963) which is one of the earliest an often cited reference for weirs.
From:
udfcd-...@googlegroups.com [mailto:udfcd-...@googlegroups.com] On Behalf Of Doug Trieste
Sent: Wednesday, December 30, 2009
8:48 AM
To: udfcd-...@googlegroups.com
Cc: 'Jerald S. Fifield'
Subject: [UDFCD-support] Is the
weir coefficient really unitless?
I was wondering if someone can provide me with a logical answer to the following associated with weir coefficients? Here is my problem.
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