# Discharge Coefficient of Valve equation

## Main Question or Discussion Point

I have a problem with Discharge Coefficient of Valve equation which is described in book 'advanced water distribution modeling and management'
let me say:

I think the expression V^2 in Discharge Equation (P. 618 of the book mentioned) is extra and the equation must be changed to:
I) Cv=V/[(2gh)^.5]
because other equation for Cv is:
II) Q=Cv (2gh)^0.5 3.14D^2/4
and these two equations are equal.
Additionally the equation P. 402 (equation 9.3) confirms my thought.
thanx

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haruspex
Homework Helper
Gold Member
So as not to restrict potential respondents to those who posssess a copy of the book, I suggest you quote the whole of the equation in question and explain the context in which each equation applies.
One possibility that occurs to me is that the v is a change in velocity of the flow before it descends height h to the valve. This might apply to the context of one equation but not the other.

haruspex
One equation says that Cv=V/[(2gh+V^2)^.5].
According to another equation: Q=Cv (2gh)^0.5*3.14*D^2/4
These two equations must be equal. Therefore insert Cv from second equation in fist equation. Then you will see the sentence V^2 in first equation is extra. Also you can compare it with another equation: Q=Cf Cv D^2 (P)^0.5. which Cf=constant.
In both of them you can see that V^2 is extra in first equation. Is not it?
Thanx

haruspex
Homework Helper
Gold Member
haruspex
One equation says that Cv=V/[(2gh+V^2)^.5].
According to another equation: Q=Cv (2gh)^0.5*3.14*D^2/4
These two equations must be equal. Therefore insert Cv from second equation in fist equation. Then you will see the sentence V^2 in first equation is extra. Also you can compare it with another equation: Q=Cf Cv D^2 (P)^0.5. which Cf=constant.
In both of them you can see that V^2 is extra in first equation. Is not it?
Thanx
As I posted, you need to explain the context: the physical set-up and what each variable means within that set-up.
It is not immediately clear that the two equations are in conflict. One of them involves Q (a volumetric flow rate) and a cross sectional area, the other does not.
Are you quite sure the two Vs in the first equation above are the same? It seems to me they should represent two different velocities.
Can you post an image of the text and any diagrams?

Hi
Cv is Discharge Coefficient of a valve which defined the relation between Q and H.
Have a look at image attached. have a look at below page too:
http://www.valvias.com/discharge-coefficient.php
No. Both V are velocity of flow.
Insert Cv from second equation into fist equation and make it simple. It is very easy to do. Then you can see V^2 is extra.
Another equation for Cv is Q=Cf Cv D^2 (P)^0.5. which Cf is constant. You can use this equation too be sure of what I believe.

http://Hi [Broken] Cv is Discharge Coefficient of a valve which defined the relation between Q and H. Have a look at image attached. have a look at below page too: http://www.valvias.com/discharge-coefficient.php[/PLAIN] [Broken] http://s6.uplod.ir/i/00777/ofsxrg0ftfbe.jpg

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haruspex
Homework Helper
Gold Member
Hi
Cv is Discharge Coefficient of a valve which defined the relation between Q and H.
Have a look at image attached. have a look at below page too:
http://www.valvias.com/discharge-coefficient.php
No. Both V are velocity of flow.
Insert Cv from second equation into fist equation and make it simple. It is very easy to do. Then you can see V^2 is extra.
Another equation for Cv is Q=Cf Cv D^2 (P)^0.5. which Cf is constant. You can use this equation too be sure of what I believe.

http://Hi [Broken] Cv is Discharge Coefficient of a valve which defined the relation between Q and H. Have a look at image attached. have a look at below page too: http://www.valvias.com/discharge-coefficient.php[/PLAIN] [Broken] http://s6.uplod.ir/i/00777/ofsxrg0ftfbe.jpg
The equation without the V2 is an approximation that is valid where the cross sectional area of the reservoir is much greater than that of the valve. In this case, we can ignore the velocity with which the level descends in the reservoir.
The equation with the V2 is correct if that V is taken as referring to the rate of descent of the level in the reservoir. It looks to me as though the distinction between the two velocities has been lost somewhere in copying from an original source.

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