Calculating amount of water passing through a headgate 2

[raklet]

I have a network of gravity-fed concrete pipes that transport irrigation water around my farm. Water enters the system at a round concrete box (4 feet diameter, 8 feet depth), and can exit the box through either of two outlets. Both outlets are controlled by adjustable round canal gates. One outlet is 24" diameter, the other is 18" diameter. The gates can be anywhere from fully closed to wide open. I would like to know how I can calculate the amount of water that is passing through each gate for any given amount that the gate is open.

Thanks,

Raklet

 

[BRIS]

The calibration of a rectangular sluice gate is difficult, circular one is far to complicated and you would be better of installing a measuring flume downstream of the gate.

But if you must - The flow is calculated by Bernoulli's equation and is simply in SI units Q = area of gate opening times velocity through the gate.
Velocity through the gate is equal to (2gh)^.5 where h is the difference in water level across the gate.
Now the difficult bits:
1) The area of flow through the gate is not the area of the opening but the area of the contracted flow (vena contracta) This you could take to be about 0.63 times the areaof the gate opening. (you need to calculate areas of segments of circles).
2) The head loss across the gate is the difference between upstream and downstream levels. If your upstream pipe is pressurised the upstream depth is the height to which the water would rise in a stand pipe. Thye water level downstream should be measured immediately after the gate.
The calibration will not be very accurate but if you use the same method for both you will get a reasonable relationship of the flow diversion.
.
(The water level downstream depends on the tail water conditions. These may either produce free flow where the water issues as a jet and there is an hydraulic jump downstream or submerged flow where the tail water submerges the jet. If you want to calculate this it is difficult. It is easiest simply to measure the water depth)

Best of luck but I wouldn’t bother attempting it !!

 

[raklet]

Thank you for the information. What does the "g"in (2gh)^.5 stand for. The calculations do not need to be very accurate. For instance: The upstream pipe is non-pressurized and is carrying 600 miners inches of water. I want to send 200 miners inches through the 18" gate and 400 miners inches through the 24" gate. Right now, I do it just by trial and error (sometimes takes a few hours to get it right). I am looking for rough approximations that will get me in the vicinity (cut down hours of adjustment to perhaps less than one hour).

Raklet

 

[cvg]

g = acceleration due to gravity 32.2 feet/sec^2

 

[itsmoked]

raklet; Is this a common desire of farmers? Getting the flows of irrigation water out of various gates and valves, or only an occasional wish?

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[raklet]

Most farmers I know probably don't care. They are content with the trial and error method - it has worked well for years. For me, the question is more academic than practical. I have a background in computer programming and network administration so my logical mind is never content with the trial and error method. I like things to be nailed down in tidy little equations and formulas.

 

[cvg]

you say you "...do it just by trial and error..." - how are you able to measure the flow diverted to each field and how do you know when it is right? Do you have a weir or flume at the end of the pipe? If not, then install one. Parshall flumes are used quite often and can be easily obtained. The Bureau of Reclamation has flow measurement information online for a variety of different types of flumes and weirs that you might use to measure the water.

Use emperical method to open the slide gate a bit, measure the opening and then go down to the field and check the flow depth at the flume. Continue taking measurements and then graph it. This would be better than trying to calculate the flow by using theoretical formulas.

 

[itsmoked]

I hear you brother.!

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[raklet]

There is a weir at the start of the system. Once the water passes the weir, it all goes into underground concrete pipe. The water can then branch two directions. The water periodically dumps into deep rectangular boxes that have pumping stations installed. The inlet pipe comes in at the very bottom of the box and the outlet is about five feet off the floor - this is to allow water to build up for the pumping stations to lift the water. Any excess water is shunted off to a holding pond. The pumping stations pump pressurized water to center pivot irrigation systems. With the pump running at 80 psi, each pivot uses 100 miners inches of water.

From experience, I know where the water level in each box should be in order to supply the pump sufficient water. Where I run into a problem is when I have to shut off several pumps on one branch and divert water to the other. Trying to balance water between the two branches is a real headache. I just want a rough estimate of how much water is flowing down each branch to make my adjusting a little easier.

 

[raklet]

When I originally set out to find out about this, I called and spoke to an engineer at the company that manufactures the headgates that I use. He told me that I should use pressure and area and sent the following message to me via email.

Ok I'll give you the easy way equate head to psi then do formula (square
root of psi x diameter raised to exponent value of 2 (diameter squared /
round orifice)x 29.82 x (pipe friction co-efficient) about .85)

It didn't make any sense to me so I turned here next. But, out of curiosity, does anyone know what he is talking about?

 

[cvg]

you could use the general orifice equation for a rough approximation. You can find this equation and full theory in Brater and King Handbook of Hydraulics.

Q = Ca(2gh)^2

Q = discharge (cu ft per sec)
C = orifice coefficient = ??
a = area (sq ft)
g = gravitational acceleration (ft / sec^2)
h = height of water above center of orifice

if you have a high tailwater condition (caused by a flat slope on the downstream side of the gate) then you need to use delta h for the water depth

I'm not sure what to use for C and it will likely vary depending upon the depth of water, size of gate and how far it is open as well as the entrance and exit conditions through your structure. It could range between .6 to .85 - it would be good to get this info from the gate manufacturer. As stated by BRIS, this is not an easy calculation, and the better way is to calibrate with actual test results using a flume or weir downstream of the gate to give an actual measurement of the flow.

 

[raklet]

Thank you all for your input. Any suggestions for placement of the flume or weir based off of my description? All water outlets are submerged - including the holding ponds - so I am not sure where to put it downstream or even if I could.

 

[itsmoked]

Ow that does make it harder. How about a regular boat speed meter. Little impeller and a meter. Then map the flow in a few places and use the channel dimensions to calculate, empirically, the flow.

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[stanier]

Down load freeware Flowpro2. It wilol take you about five minutes to calculate it.

Geoffrey D Stone FIMechE C.Eng;FIEust CP Eng

http://www.waterhammer.bigblog.com.au

 

[katmar]

Raklet, the analyses offered so far overcomplicate and oversimplify the situation at the same time. Using an orifice calculation is unnecessarily complicated. Rather treat the gate as a valve. For your purposes you can regard the flowrate through the valve as Q = Cv x SQRT(head). The constant Cv is called the valve flow coefficient. The Cv is a function of the fraction of full open for the valve, but remains "constant" at each position as the flow and head change.

I would draw up a calibration curve for each gate alone. Seeing that you have a weir upstream and you know the total flow, you could close one gate completely and plot the head (height in supply well) against the flow for various fractions of full open for one gate at a time. From this plot you could calculate a Cv for each fraction of full open, and draw a graph to allow interpolation. It does not matter what units you use for Q (flow) or for head as long as you stick with these units once you have calculated your Cv's. Obviously there are many combinations of valve openings for the two gates and head that will give the same flow. Quite honestly, if I were in your position, I would do it once by trial and error and then make marks on the gate stems to allow them to be easily reset the next time!

But this analysis is also an oversimplification in that the flow through each branch is a function not only of the gate position, but also of the piping geometry. I have never worked with miners inches before, but from what I can find with a quick Google search it seems to be equal to about 0.025 cubic ft per second? If this is so then the pressure drops you will experience in your piping will be relatively low, and maybe this simplification is good enough. To do it properly would require many more calculations and would take this exercise out of the "intersting diversion" category.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[blueoak]

As mentioned earlier the Bureau of Reclamation are about the best source for this. Check out their 3rd edition of the Water Measurement Manual at:

http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/wmm.html

Your local NRCS or Bureau of Reclamation office would probably be happy to help too.

My question is if you are using center pivots why don't you install pressure regulators. You can increase your efficiency and so long as you are meeting the require pressure you can drop back the pump to save fuel and always know your flow rate. Call the NRCS and see if you can get EQIP or some other funding to help.

As far as the comment about farmers not caring, that depends on where you are. Try the much of the central valley of california, west kansas, or much of texas and I am sure they know to the tenth of an inch how much water they applied that year. It's all on where you are.