What’s the capacity of a vertical pipe?

This is a question that comes up quite often, and I usually tell people that it depends on the water depth over the pipe entry.
This means that we either use the weir or the orifice formula.

 

Or if the pipe is flowing full, as in a syphonic system, we can use the pipe flowing full formulas, Colebrooke-White etc,  and work out the pipe size using the hydraulic grade.

However this is not necessarily always the case.

What if water enters a downpipe from lower level roofs, balconies etc?
A plumbing stack has this situation all the time.

 

So now we can start to have some real fun.confused

When water flows down a vertical pipe (assuming it is not designed as syphonic) the pipe does not flow full.
There is also air being pushed down, and air trying to rise up.
This is why plumbing stacks have vents all over the place, to relieve any unwanted air pressures.
Storm water pipes have entries all over the place which do the same thing.

 

Water starts out clinging to the sides, and as the flow gets greater it starts to spiral, and getting greater still starts to oscillate, forming plugs. Rapid oscillations develop unwanted noise and vibrations.

 

It has been determined (refer Standard Plumbing Engineering Design by Louis S Nielsen) that a flow which occupies about 1/4 to 1/3 of the cross sectional area of the downpipe flows without a problem.

 

The next thing then is to find out the terminal velocity so we can work out the flow.
We don’t need to go into that, suffice to say, that I have reduced all the formulas from the above text into something simple.
This is what can be referred to as a recommended maximum flow based on the above concepts, and equates to a flow that occupies 7/24 of the DP area.

 

So      Q = 0.00004 * dia^2.666   where Q is in L/s, and dia in mm.

 

This equates to an inground pipe of the same size with a grade of about 1:100.

 

So, there you go, just don’t make any inground pipe smaller than the DP.

Want to impress your clients?

Turns out this is not an exact science, but just for the sake of BS..ing at design meetings, terminal velocity is about 5m/s and it takes about 2 stories to get there.

6 comments

  1. Raymond Ho says:

    Dear Dr Ken

    I have been reading your articles many years. Thank you for your generosity. I use your free programs since 2010. In more than two decades, I found rarely other website can provide the same benefits as yours. Like to see more your interesting articles to come.

    Have a nice day.

    RH

  2. Anonymous says:

    Hi Ken,

    I’m impressed for your vast knowledge and years experience. You’re great!

    May I ask you for designing surface stormwater on suspended slabs, can I use stormwater pits?

    Good wishes.
    Raymond

  3. Samir says:

    Hi Ken,

    Trust this finds you well.
    I have a question in regards to the maximum flow capacity or volume flow rate within a vertical pipe (with no bends introduced). Is it safe to utilize the formula CxAx ((sq.rt (2gH)) to determine this value.
    C = pipe coefficient
    A = area
    g = gravity
    H = height
    The sole purpose of this, is to determine how many pipes can be connected to that specific pipe without exceeding the maximum allowable velocity!

    • Hi Samir,
      No you can’t use that formula for that purpose.
      That is the orifice formula, and is used to determine the flow that can get through the entry ‘throat’ of the DP.
      ie the orifice.
      The H in the formula is the head over the orifice not the height of the DP.
      ie the depth on water on the roof, or in the gutter.

      The ‘theoretical’ max flow capacity ‘Q’ is given in the blog.
      You can rearrange this formula to get the DP dia from a known flow.

      The max flow velocity in a vertical pipe not flowing full is the terminal velocity.
      The code max velocity requirements relate to graded pipes only, as this has a large effect on the head (friction) loss.

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