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I'm calculating TDH (Total Dynamic Head) for the purpose of replacing my sump pump. I also need to replace the discharge line (pvc + check valve), however, the structure is forcing me to a very specific system path.

So, I want to make sure my new pump's "Max Head" rating is greater than the TDH of my system. Below I've provided my TDH calculation process, specs/inputs, calculations, and constraints.

Could you please check me on these calculations and correct me if I'm wrong anywhere?

Process:

  • TDH = Static Head + Friction Head

Finding Static Head...

  • Static Head = Sum of Verticals
  • Vertical A: 8 ft - this is the Sump Pit Depth (up to basement floor)
  • Vertical B: 2.5 ft - this is distance from basement floor to the height of the discharge exit
  • Static Head = 10.5 ft

Finding Friction Head...

  • Friction Head = ( ( Actual Pipe Length + Equivalent Length of Pipe ) * Friction Loss ) / Actual Pipe Length

Finding each of the inputs to Friction Head below..

  • Actual Length of Pipe = 4 ft + 3 ft = 7 ft
    - 4 ft for horizontal length of pit to next vertical pipe. 3 ft for length from next elbow through the exit point and to the final elbow.
    - For this value, I include only horizontal pipe lengths to the last elbow (outside, after the point the pipe enters a decline and gravity takes over). I do not include the vertical pipes. Please, correct me if I'm wrong and should be including vertical pipe length.

  • Equivalent Length of Pipe = (4 ft * 4 elbows) + 13.4 ft * 1 check valve = 29.4 ft
    - (all 1-1/2")
    - 4 ft for each 90 degree elbow
    - 13.4 for check valve

  • Friction Loss Coefficient = 13.45
    - This is where I'm most uncertain. In the friction loss coefficient table I'm seeing, this is the value when referencing my pipe diameter (1-1/2") and GPM. I'm not sure where I'm supposed to find this GPM.
    - Is this the desired GPM, as in, the maximum rate at which water could be entering the pit? Or is it supposed to be the sump pump's GPM?
    - If it's the pump's GPM, then should it be the mfg's rated max GPM? i.e., on a performance curve, the GPM when TDH = 0. Or should it be the GPM in my system, i.e. not theoretical max? If the latter, this seems a little recursive/circular. How can I know what GPM is without TDH?

  • Friction Head = ( ( 7 ft + 29.4 ft ) * 13.45 ) / 29.4 ft = 16.65 ft

Finally, using Static Head and Friction Head, I calculate TDH...

  • TDH = Static Head + Friction Head = 10 ft + 16.65 ft = 26.65 ft

As such, in my system with a TDH of 26.65, a sump pump must be rated for a max head of greater than that value.

A model with less, such as the Zoeller 1/2 hp 1075 model with a max head of 25 ft, would not be an option because we would expect it to fail. This pump a simpler system of the same vertical but the elbows add too much to the Friction Head.

Hard constraints of the system...

  • My sump will need an NPT of 1-1/2", as such, the PVC system will be 1-1/2"
  • I cannot change the sump pit depth or the discharge exit point
  • Due to the structure between the sump pit and the discharge point, the # of 90 degree elbow fittings are necessary. I cannot and do not want to remodel the house to accommodate less 90 degree turns. Acknowledging that I could use two 45 degree elbow for each 90 (and very well may, if necessary), the main goal here is just to make sure I'm calculating TDH correctly (thanks for the patience).
  • The discharge exit point (leaving the house), runs outside and then must immediately take a hard 90 degree left using an elbow. At that point, it can run downhill (in the PVC) for 20 feet into the backyard. This is necessary/can't be changed. At this last elbow, I exclude the PVC from the calculations because gravity takes over for the pump. (Please, correct me if I'm wrong).
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  • Pretty much you have to pick a number for GPM to calculate - or perhaps pick and calculate several. What actually happens is that your actual pump will arrive at an actual GPM which will be due to the friction head + static head at that point matching what your pump can do. The pump's rated max GPM is often rated at zero head, so not usually the right number to pick. Vertical pipe absolutely contributes to friction head.
    – Ecnerwal
    May 26 at 17:37
  • The friction is no big deal until you reach much higher flows but the static head is what kind of flows are you expecting with a 1-1/2” discharge that’s a lot of volume
    – Ed Beal
    May 26 at 19:33
  • @Ecnerwal Thanks for the response. That makes sense! After reviewing the math again, I realized that I incorrectly interpreted the formula for calculating Friction Head, itself. In the formula, the denominator is not supposed to be "Actual Pipe Length" but a constant of 100 ft, as the Friction Loss Coefficient from the tables are for 100 ft increments. It was confusing because in the guide + chart, I referenced didn't note that these coefficients were for 100 ft increments, and their "actual pipe length" sample value was 100 ft, so I mistakenly conflated the two.
    – JohnX
    May 27 at 15:41
  • @EdBeal Yeah, I think you're right. See my comment to Ecnerwal, ,where I realized that I had the formula incorrect for Friction Head, resulting in a value 6 times larger than it should have been.
    – JohnX
    May 27 at 15:45

1 Answer 1

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There are multiple TDH calculators on the web, some more easily useful than others. Picking one more or less at random and finding it "not utterly insane to use" I ran a few numbers, not making various assumptions about "don't count this pipe" and taking your word for the check valve and elbow contributions, rather than looking those up myself, as they seem plausible.

Running your system with 10 feet elevation differential, 70 equivalent feet of 1.5" plastic pipe and 1 GPM, I get 10.01 ft head.

At 10 GPM I get 10.68 FoH

15 - 11.44

20 - 12.44

25 - 13.69

30 - 15.18

Picking another, I get the same numbers.

Unless you have some insanely large pumping rate in mind, friction head is unlikely to be a particularly big deal here. I'm guessing you made a math error, I'm not going to try and sort it out. Here's a third, which also agrees.

I have to go to 56.5 GPM to hit your TDH number, and that's with a great deal more pipe than you were counting.

Conveniently, the pump you mention happens to do 30 GPM at 15 ft head. Just about perfectly matched.

If "pump life" is your "thing you want to maximize" and you know your maximum inflow rate, choosing a pump that is only a little faster than that rate (at the TDH you compute, iteratively, for it) (so as to minimize starts & stops) would help, according to conventional wisdom that stopping and starting pumps is the thing that wears them out the most. If you don't know the inflow rate, at least adjusting your floats for maximum storage before starting the pump (so it pumps more water, less often) would be a step in the same direction.

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  • Thank you, @Ecnerwal! As I said in my other comment, I found the issue with my process, however, this is actually very helpful information outside checking the math, particularly that last piece.
    – JohnX
    May 27 at 15:47
  • JohnX the thanks is given by upvoting or acceptance of an answer. the check mark you can see next to the up down arrows this actually helps others find an acceptable answer with a similar question.
    – Ed Beal
    May 27 at 18:52

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