# How to calculate TDH of PVC downspouts and water tank height?

• saxman2u
In summary, this diagram shows how to calculate TDH for a rainwater catchment system. You need to enter the tank from the bottom (or low on the side), calculate the head loss, and add it to the pressure at the discharge point.
saxman2u
Greetings,
Looking for the best way to calculate TDH for some rainwater catchment systems I am designing in Texas. Some homes we are installing these systems on have large footprints, between 6,000 to 8,000 sq feet. The large rainwater collection tanks we install range between 30,000 and 65,000 gallons and are 7 feet tall. The PVC pipe entering the top of the tank is around 8 feet high. Most soffits/fascia/gutter bottoms are around 8 feet high, so you can see that it is ideal to place a tank for a large home downhill when using 4" PVC pipe. The downspouts for the collection system are all made of PVC pipe, and are primed and glued all the way to the tank so that the system is sealed. The worst case scenario would be to install a tank for a large home and in a heavy downpour, more water backs up into or even our of the gutter rather than goes into the tank because of pipe friction loss. That is a hard repair/fix! I use a 4" rain rate/hr for my calculations to accommodate heavy steady rain but to also not "over design/size" the system for cost.

An example we could use would be 120 GPM that is being collect at the last downspout or closest downspout to the tank, downspout F. The farthest downspout from the tank is downspout A and it only collects 20 GPM from its section of roof area. If the closest downspout to the tank or downspout F is 100 ft from the tank, and the farthest downspout or downspout A is 500 ft from the tank, I get .81 TDH at downspout F and .55 TDH for downspout A. Will the water in downspout A ever rise above .15 ft during a 4" steady rain event?

The downspout that is farthest from the tank has the least amount of water in it but has to travel the farthest. As the conveyance pipes pick up downspouts, more water is flowing in the system. The last downspout (or closest downspout to the tank) has the most water moving past it or in it since it is a culmination of all the downspouts/roof area. My question is, when calculating TDH, what distance do I use? Should I use the distance and elbows from the tank to the tank's closest downspout to figure out how much head will be in the pipes? Or, should I use the distance from the tank to the farthest downspout? Also, what GPM should I use for the farthest downspout? I need to build in some buffer but I also want a CYA for my systems. I was just thinking of using the farthest downspout with max GPM and call it a day, but then again, my mind now wants to know what is actually happening in the pipes but I also want to design my systems appropriately and build tanks at an elevation that is reasonable accurate based on fluid hydraulics. I need some clear PVC pipe I guess!

Thanks!
-S

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If I understand correctly, this diagram is a simplified version of your system. I'm assuming that the tank is open to atmosphere, and the water drops into the tank (pipe outlet is not submerged).

You have flow rates, pipe lengths, and number of elbows from B to C, from A to C, and from C to D. Start at D, where the pressure is zero. Calculate the head loss from C to D. That's your pressure at C. Now calculate head loss from B to C, and add to the pressure at C. If the total is less than the vertical distance from B to D, the pipe is flowing properly (not overflowing). Repeat for A to C, then add for A to D.

The key is start at the discharge and work upstream. The pressure at C is determined only by the flow through C. After you wrap your mind around that, everything else will fall into place.

You need to 'work back' from the tank. At 20 GPM/4", it's unlikely that you'll flood at 'A,' but it's entirely possible that water from 'A' will cause a flood at a downstream location. Relative elevations and distances...

(possibly) useful note:

If you enter the tank from the bottom (or low on the side), your static head will be low when the tank is low. Entering from the top 'gives away' that free advantage. Couple that with a 'waste-relief' standpipe(s) arrangement (at the house) and you can have a system that will collect maximum water when the tank is low and overflow in a controlled manner when the capacity is exceeded.

saxman2u
jrmichler said:
If I understand correctly, this diagram is a simplified version of your system. I'm assuming that the tank is open to atmosphere, and the water drops into the tank (pipe outlet is not submerged).
View attachment 250882
You have flow rates, pipe lengths, and number of elbows from B to C, from A to C, and from C to D. Start at D, where the pressure is zero. Calculate the head loss from C to D. That's your pressure at C. Now calculate head loss from B to C, and add to the pressure at C. If the total is less than the vertical distance from B to D, the pipe is flowing properly (not overflowing). Repeat for A to C, then add for A to D.

The key is start at the discharge and work upstream. The pressure at C is determined only by the flow through C. After you wrap your mind around that, everything else will fall into place.
Thanks for the response. The picture is a good representation of some of our systems.

Let's assume that 4" standpipe B has 20 GPM flowing into it, and at point C, there is 120 GPM in the line. Distance of C to D is 100' with no turns/elbows. Distance of C to B is 8 ft. Head loss at point C is .81 ft? For the segment B to C, if the picture is an actual representation, just a vertical pipe that is connected to main conveyance line, how do I calculate head loss of the B to C segment if it is not full of water?

Thank you.
-S

'Head Loss' in the downspouts (like B-C) is effectively moot (as jrmilcher implies). You can't collect enough water for them to be a problem (in a system where the downspouts are the same size as the drain pipe). If the total head (the sum of elevation and friction head) is less than the elevation at 'B,' you can ignore it. If the total head is more than the elevation at 'B,' you're flooding. Either way, what happens at B depends on the downstream conditions (not on the downspout). I'm not even sure that 'head loss' has any meaning for water essentially free-falling down a vertical pipe.

ok, I think I am getting it. Most tanks are at the same grade or lower than the house. In the attached drawing, pardon my chicken scratch, the tank is 2 ft below the house, and the downspouts are 7 feet tall. The pipe entering the tank is 8 feet tall, therefore, the differential (distance between tops of downspouts and pipe entering tank) is only 12 inches. If I did the calculation correctly and took into account the 6 ft and 8 ft increments of the downspouts that are full of water, then downspout B will overflow .24 inches since its TDH is 1.24. Downspout A should not overflow since its TDH is .51. I know I did not take into account elbow, but I am just trying to get the jist of this calculation. In this case, we should design the system for the tank to be another foot lower or raise the house!

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Will mosquitoes and other insects be a problem in the standing water remaining in the piping?

You're getting there, but something still doesn't look right with your numbers. Are you using a 'common' pipe to the tank, or are these independent runs? If it's a common pipe: for the case of equal flows at the downspouts (50 GPM) and equal elevations of the downspouts, the upstream downspout will be the first to flood. The head at 'A' should be equal to the head at 'B' plus the friction loss in the 50GPM/100' of pipe (always higher than 'B').

Dullard said:
You're getting there, but something still doesn't look right with your numbers. Are you using a 'common' pipe to the tank, or are these independent runs? If it's a common pipe: for the case of equal flows at the downspouts (50 GPM) and equal elevations of the downspouts, the upstream downspout will be the first to flood. The head at 'A' should be equal to the head at 'B' plus the friction loss in the 50GPM/100' of pipe (always higher than 'B').
Ok, I understand now. yes, using a common pipe to the tank. I redid my math, here goes: Pipe A should have 50 GPM at 106 linear feet which is .17 feet of head before it joins the next downspout. When the two pipes merge, now more head is going to pipe A, so it would be 100 GPM at 208 linear feet producing 1.21 feet of head. Add .17 and 1.21 to get 1.38 feet of head for pipe A. The water actually backs up or overflow pipe A first. I recalculated head for pipe B and it should be 1.22. I under stand that I need to also include friction loss for the elbows as well. let me know if this seems correct, thanks!

Tom.G said:
Will mosquitoes and other insects be a problem in the standing water remaining in the piping?
No, with these systems, rainwater catchment installers will install a valve at the bottom/end of the line close to the tank so that the client can empty the system after the rain event.

We have actually developed a computerized or automated system that flushes the initial water that hits the roof as well as draining the system once the rain event is over. It uses a small arduino board, optcial rain sensor, and electronic valve. We have had great results so far and our client like collecting cleaner water with less maintenance.

Adding mesh screens to the gutters also keeps bugs and debris out of the gutters.

-S

Tom.G
I think you got it.
If you re-read post #3, you can probably now see the advantage of entering the tank from a low point - the water level in the tank replaces the '8 ft' elevation that you're stuck with when entering at the top - You can collect a lot more water when the tank is low. This could complicate the 'cleanup' protocol (described in post # 10) - you'd have to add a blocking valve at the tank inlet. I guess it comes down to how often/hard it rains.

I read Post 10 as saying they already put the block valve in the line to the tank (so the owner can drain the lines after the rain stops). In that case I think the valve would normally be closed (?), and then you might as well enter the tank down at the bottom, saving that 8 feet (as @Dullard suggests in Post 11).

Entering the tank at the top avoids problems caused by leaky valves / fittings, or operator errors. But burying the tank to gain that head is going to be expensive.

Dullard said:
I think you got it.
If you re-read post #3, you can probably now see the advantage of entering the tank from a low point - the water level in the tank replaces the '8 ft' elevation that you're stuck with when entering at the top - You can collect a lot more water when the tank is low. This could complicate the 'cleanup' protocol (described in post # 10) - you'd have to add a blocking valve at the tank inlet. I guess it comes down to how often/hard it rains.
Yes, this all makes sense. On smaller properties, there is usually not enough elevation difference to get the tank that low. Remember, we are talking about tanks that are 30-40 feet wide, 30,000 to 55,000 gallon tanks. On some properties, the elevation is almost the same which makes it hard. Excavation also gets expensive too if you want the tank low. Above ground tanks can be assembled quickly and are cost effective as well. You can see these calculations are critical when designing these systems. Once the tank is built, and someone makes an elevation error or a client calls back and says that their gutters overflow all the time (this has not happened in my case), you either have to lower the tank, raise the house, install larger pipes to overcome friction loss, set up a smaller tank and then pump all the water, or eliminate some downspouts. None of these are good solutions by any means.

I don't have the time to calculate the head at each downspout for these big projects, I can't get bogged down in that. Irrigation guys have computers that can calculate their head and pump requirements and pipe size for their irrigation systems which makes it easier for them. I am going to look back at a couple of projects and look at the furthest downspout, and do the math both ways, what the actual head is, and then, just use the total GPM and the farthest downspout. It might not be that much of a difference, but then I know I am covered or CYA and it builds in a little more room for a heavy downpour of over 4"/hr rate rain event. So, for example, instead of calculating pipe A at 50 GPM, i would use 100 GPM at 314 linear feet of pipe. This gets me 1.82 feet of head, about 6" more of head, which is not that big of a difference IMO. Let me know what you think. Thanks.

-S

Sorry, have you explained how you are calculating your head loss terms (like the 1.82 feet for 314 feet of 4" pipe)? I just went to the Crane 410 book, it has a table. This gives slightly higher head loss values (almost 2 feet for that case).

Also note, this is just for friction so you might want to include fittings and the valves. As I recall, each elbow is 30 diameters (or 10 more feet for 4 inch pipe). As you point out you have just one chance to get it right so you might be wise to up the numbers by 10 or 20 percent. Another approach would be to build with 6 inch pipe vs 4 inch. Obviously more expensive to install, but it cuts the head losses by a factor of 8. I would ask myself how much extra that would cost, considering the customer is buying a 55,000 gallon tank.

gmax137 said:
Sorry, have you explained how you are calculating your head loss terms (like the 1.82 feet for 314 feet of 4" pipe)? I just went to the Crane 410 book, it has a table. This gives slightly higher head loss values (almost 2 feet for that case).

Also note, this is just for friction so you might want to include fittings and the valves. As I recall, each elbow is 30 diameters (or 10 more feet for 4 inch pipe). As you point out you have just one chance to get it right so you might be wise to up the numbers by 10 or 20 percent. Another approach would be to build with 6 inch pipe vs 4 inch. Obviously more expensive to install, but it cuts the head losses by a factor of 8. I would ask myself how much extra that would cost, considering the customer is buying a 55,000 gallon tank.
I have been using this online calculator:

I agree with you about the valves and fittings, I usually add another 20% of linear feet to accommodate for this, thank you for bringing that up. I also agree with you on the 6" pipe and we do use that at times. Is there an online TDH calculator that you suggest?

-S

I can't use online calculators in my line of work. We use Crane Technical Paper No. 410 "Flow of Fluids Through Valves, Fittings, and Pipe." But really the information is available in lots of places, for example the pipe manufacturer's catalogs, or mechanical engineering books. The numbers you get with your calculator are very close to what I got using the Crane Table -- It is for flow of water thru sch 40 steel pipe. If your calculator let's you enter PVC rather than steel, that might account for the differences. Is the relative roughness of PVC a little smoother than commercial steel?

All of these calculations are estimates really, normal practice is to build some margin into the actual design as discussed above.

I vote for the 6-inch pipe idea -- One customer with overflowing gutters could cause a lot of bad press. But then I'm not paying the bills .

gmax137 said:
I can't use online calculators in my line of work. We use Crane Technical Paper No. 410 "Flow of Fluids Through Valves, Fittings, and Pipe." But really the information is available in lots of places, for example the pipe manufacturer's catalogs, or mechanical engineering books. The numbers you get with your calculator are very close to what I got using the Crane Table -- It is for flow of water thru sch 40 steel pipe. If your calculator let's you enter PVC rather than steel, that might account for the differences. Is the relative roughness of PVC a little smoother than commercial steel?

All of these calculations are estimates really, normal practice is to build some margin into the actual design as discussed above.

I vote for the 6-inch pipe idea -- One customer with overflowing gutters could cause a lot of bad press. But then I'm not paying the bills .
This is great information. I am not sure about if the PVC is smoother than steel. I looked at a few different online calculators and they all came out to be the same. I did choose plastic/PVC as the material when using the calculator. There is a choice for 4" steel and the TDH is higher, so, the PVC does seem smoother.

About the margins, i agree with this too. I use a 4" rate event for my calculations. Maybe I can bump this up to a 5" sustained rate event, and/or use my method of using the furthest downspout from the tank and use total GPM for the PVC pipe from the farthest downspout all the way to the tank entry point. Thoughts on this?

Some jobs require over 1500 feet of pipe, and there is a considerable cost difference between 4" and 6" PVC, as well as labor. I try to stick with 4" since it is more manageable with 2 guys and cheaper. However, if 6" is needed, I can just build that into my proposals.

saxman2u said:
About the margins, i agree with this too. I use a 4" rate event for my calculations. Maybe I can bump this up to a 5" sustained rate event, and/or use my method of using the furthest downspout from the tank and use total GPM for the PVC pipe from the farthest downspout all the way to the tank entry point. Thoughts on this?
Your approach (total GPM from the furthest downspout) seems to be conservative and will provide margin.

Some jobs require over 1500 feet of pipe, and there is a considerable cost difference between 4" and 6" PVC, as well as labor. I try to stick with 4" since it is more manageable with 2 guys and cheaper. However, if 6" is needed, I can just build that into my proposals.
Wow, 1500 feet of pipe is more than we have been talking about. I would say for a job that big, some detailed engineering is called for (remembering, "engineering is doing with 50-cents, what anyone else can do with a dollar"). I'm still curious as to the installed cost of these big cisterns, and the relative costs of the tank and the piping.

## 1. How do I calculate the total dynamic head (TDH) of PVC downspouts?

To calculate the TDH of PVC downspouts, you will need to determine the vertical distance from the top of the downspout to the discharge point, as well as the horizontal distance from the downspout to the discharge point. Once you have these measurements, you can use the following formula: TDH = √(vertical distance)^2 + (horizontal distance)^2. This will give you the total dynamic head in feet.

## 2. What is the importance of calculating TDH for PVC downspouts?

Calculating the TDH of PVC downspouts is important because it helps determine the amount of pressure that will be needed to pump water through the downspout system. This information is crucial for selecting the appropriate pump and ensuring efficient water flow.

## 3. How do I calculate the height of a water tank based on TDH?

To calculate the height of a water tank based on TDH, you will need to divide the TDH by the specific gravity of the fluid being pumped (typically water has a specific gravity of 1). This will give you the total head in feet, which can then be converted to the height of the water tank in feet or meters.

## 4. What factors can affect the TDH calculation for PVC downspouts?

The TDH calculation for PVC downspouts can be affected by several factors, including the length and diameter of the downspout, the number of bends or turns in the system, and the type of pump being used. These factors can impact the pressure and flow rate of the water, and therefore, the TDH calculation.

## 5. Are there any online tools or resources available for calculating TDH of PVC downspouts and water tank height?

Yes, there are several online calculators and resources available for calculating TDH of PVC downspouts and water tank height. These include manufacturer websites, engineering websites, and online pump selection tools. It is important to ensure the accuracy of the information and calculations from these resources before making any final decisions for your specific application.

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