Hi,
I'm trying to model a valve that discharges to the atmosphere for environmental purposes.
The emitter equation: q=Cpg.
Firstly is C (discharge coefficient) also known as Cv (flow coefficient imperial)?
If I have Kv (flow coefficient metric) does this need to be converted to Cv?
In the help menu it says g (pressure exponent) is 0.5 for nozzles/sprinklers. Would this also apply to a 350mm valve with 60m of 350mm discharge pipe?
Thanks,
Cliff Dredge.
Cliff,
The emitter coefficient C or sometimes called Ce in our help files is not the same as Cv
Emitter Coefficient Units (C or Ce)are generally expressed in US units as “flow units / (psi)1/2 ” and in SI Units as “flow units / (meters)1/2 ”.
While other values for the pressure exponent "g" (Note I can't properly show the greek gamma on here which is what "g" represents) can be used, for nozzles and sprinkler heads g equals 0.5 and the manufacturer usually provides the value of the discharge coefficient in units of gpm/psi0.5 (stated as the flow through the device at a 1 psi pressure drop). Deciding to use a different value is always an option but without any other information the default value used is usually 0.5 unless you have better information from the manufacturer.
If you wish to use a different pressure exponent value that 0.5 this is changed in the simulation options under the demand tab as the "Emitter Exponent" but is a global setting for all emitters.
Simulation options - Demand tab - Emitter Exponent location (click if need larger image)
Emiter exponent - pressure exponent.jpg
However, the emitter in the model should generally be placed at the end of the discharge pipe not at the location of the valve so that it represents the actual location of the discharge.
As far as relating Ce to Cv that part get's a bit technical and can be a bit confusing due to the different terminology often used for the key terms. I would highly suggest referring to fluid dynamics texts if you wish to get into further detail on that.
Here is a link that appears to have some calculators in it for getting Cd from Cv or Kv that may help, but use these at your own risk as we have not verified these calculators:
http://www.valvias.com/flow-equation...fficient-c.php
Theory: http://www.valvias.com/discharge-coefficient.php
Originally Posted by Cliff Dredge
Last edited by Patrick Moore; April 21, 2016 at 12:24 PM.
Thanks Patrick. I'm sorry I still have confusion here:
As you have stated the emitter/discharge coefficient (Ce/Cd) are dimensional values of (SI) = flow/(m)^0.5. Although the 'valvias' resource indicates Cd is a dimensionless value, which doesn't make sense with the H2O equation q=Cd*p^0.5
For example I have a Kv of (310L/s)/98.1m(1bar). So I can work out Cd to be (31.29L/s)/(1m^0.5). 310=31.29*98.1^0.5
If I use the valvias calculator I get a dimensionless value = 0.4465?
From my research it seems the discharge coefficient is dimensionless although in H2O it is dimensional and just wanted some further clarity on the matter?
Cliff Dredge.
Cliff,
Thanks for your response. Admittedly, this is why we have referred you to hydraulic texts for more in depth answers. But the emitter equation "C" does have units as noted above.
Q = C * p^g so by rearranging we find C = Q/p^g
From the equation Q (units of Length^3/time or Flowrate units) and p^g is (pressure units)^g so C is in Flowrate/pressure unit^g power or is g = 1/2 then it is in units of Flowrate/pressure^1/2.
As I can't find a derivation of where the emitter equation comes from to verify the C used, all we can do is verify the units shown in modeling texts regarding use of emitters like the EPANET helpfile that for emitters is essentially repeated in the Innovyze H2OMAP Water and InfoWater help files.
From the Orifice equation which does use Cd (the coefficient of Discharge) (Pulling this equation from this website: http://engineering.wikia.com/wiki/Orifice_equation)
The orifice equation describes the rate of flow of liquid through an orifice.
The equation can be represented as:
where Q = flow (cubic metres per second)
C(d) = coefficient of discharge
A = area of orifice (square metres)
g = acceleration from gravity (9.81 m/s^2)
h = head acting on the centreline (m)
So the Cd rearranging is Q/(A*sqrt(2gh)) and noting Length as "L":
now G is in L/time^2 and if H is in L the sqrt (2gh) term is sqrt(2*L/time^2 *L) or sqrt (2*(L/time)^2) which is just units of L/time.
Area is in units of L^2 so the denominator is L^2*L/time or L^3/time which is the same unit as flow and causes Cd to be dimensionless as noted.
A such that seems to show that the "C" in emitter equation is thus not the same Cd in the orifice equation as one has to have units ("C") and one has to be dimensionless ("Cd").
For modeling purposes, regarding what is entered in the model, you are asked to enter the "C" value from the emitter coefficient and not the Cd value.
Hope this helps.
Patrick
Last edited by Patrick Moore; April 26, 2016 at 12:30 AM.
Thanks Patrick. Apparently there's a text for water distribution developed by Innovyze. Do you know what this is and would it answer all my hydraulic queries?
Cliff Dredge
Cliff,
The book I would recommend is The Comprehensive Water Distribution Systems Analysis Handbook 2 ed by Boulos/ Lansey/ Karney.
Comp Water Dist Systen Analysis Handbook -cover.jpg
I hope it helps and sent you directly by email a small excerpt on emitters for you to preview.
But, only you my friend would know if it would answer all your questions! ;-)
Patrick Moore
Cliff,
For the benefit of other users, I wanted to post this excerpt from the book noted above as well as it explains what the "C" in the emitter coefficient represents and how it is derived.
Excerpt from pages 3-25 and 3-26 of the Comprehensive Water Distribution Systems Analysis Handbook regarding emitters. (click for larger image if necessary)
Emitter Equation development.jpg
According to this, The Cemit which represents the emitter equation "C" referenced above is essentially related to the Cd (which is noted as the discharge coefficient for total head or Cd' for the discharge coefficient for total pressure) and the area of the opening. However, in the equation shown Cd would necessarily seem to need to have some other factors wrapped up into it such as the "Sqrt (2g)" term not shown so that the Cd would remain unit less as was shown from the Orifice equation which this is based upon.
As such the Cemit term should essentially be Cd' *sqrt(2g)*Area and this would leave you with Q = Cemit*pg from the orifice equation Q= Cd*A*sqrt(2gh) with some correction in the Cd' from Cd so the units work out correctly when you change the h from Head to p for pressure. It would seem if you also include the equations showing the relationship of Cd to Cv you could calculate the Cemit using Cv instead of Cd as well which is what the InfoWater UDF User Guide uses.
But by combining the orifice equation ( Q= Cd*A*sqrt(2gh) ) and the emitter equation (Q = Cemit*pg ) and solving for Cemit you can essentially derive the equation you can use to calculate the emitter coefficient similar to what is shown in the InfoWater UDF User Guide for US units. This should allow you to derive the equation to use in SI units. The key is that you need to convert the h value and p pressure value so those drop out and you are left with essentially something like Cemit = Cd *sqrt(2g)*Area*(conversion of h1/2 to p1/2) [note: I believe they intend Cd' = Cd*(conversion of h1/2 to p1/2) but I have not been able to verify this for sure]
If you assume a round opening you can simplify the equation to be a function of the diameter of the emitter opening, the Cd (or Cv), and unit conversions to get the needed final units. Cemit = Cd*X*D2 where X is the unit conversion and other factors.
Anyway, thought this might help others so I posted it here.
Patrick Moore
Last edited by Patrick Moore; April 28, 2016 at 10:54 PM.
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