# 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.

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.

# How does a CFD simulation of a Box Gutter compare to the Plumbing Code

WHAT IS CFD

CFD stands for Computational Fluid Dynamics.

It is a way of generating a computer simulation of fluid flow in real time.

It consists of analyzing all forces on individual particles in the fluid. The forces can consist of gravity, viscosity, friction, surface tension, shear forces, density etc. (Nothing to do with the standard hydraulic empirical formulas.)  The resultant of these forces on each particle is distributed to surrounding particles, and so on. The resulting equations must also satisfy  the conservation of mass, momentum and energy.  This means millions of calculations for each frame of a video to determine how far, and in what direction, each particle will move in a given time frame. If there are 25 frames/second, a ten second video will have 250 frames, with millions of calculations for each frame.

Each fluid particle is called a cell. The smaller the cell the more accurate the simulation, (generally). The division of the fluid into cells is called a mesh. There are millions of cells in the mesh.

The cells can be a combination of hexahedral, tetrahedral, prismatic, pyramidal or polyhedral elements.

It is a hugely time consuming process if you wish to use it in any serious way. For instance I did a CFD simulation of a much simpler thing than that shown above, and using 16 cores of computing power it took 30 hours to get a result. (and a similar amount of time to analyse the result). However I could then read the pressure, velocity, and depth anywhere in the simulation, and all in pretty colours. But this is a huge overkill for the design of a simple box gutter.

The simulation you see above took 4 hours of computer calculation, because I used a very coarse mesh. However the result is good enough to visualize what is going on, and to prove a point.

ANALYZING THE RESULTS

The above simulation is very pretty, but not very good at measuring any meaningful depths. So lets take a closer look at the mesh.

The important things to note are:-

a) The deepest flow is at the upstream end, because the water surface must always fall in the direction of the flow.

b) The flow over the brink is 0.7*critical depth. This is a hydraulic principle of a free outfall from an open channel.

c) The downpipe does not flow full. The flow is restricted by the entry throat diameter.

WHAT ARE THE CODE RESULTS

The simulation is based on 11 L/s, with a 300mm wide box gutter, and no slope.

From the Plumbing Code, Fig I1 gives the gutter depth for no slope as 170, and with 1:200 slope, depth =  145 mm.

AS3500.3 Fig I1 for 11 L/s

From fig I3, for a DP dia of 125, flow = 11 L/s rainwater head details are :-

• depth of water = 112

• Total depth of RWH = 187,
• and length of RWH, at BG depth of 145 (1:200) = 173

From Fig I6 :-

Critical depth “Loc” = 52 mm

0.7 * critical depth = 37

PLOTTING THE RESULTS ON THE MESH

The background grid is 100mm spacing, so you can visually check the dimensions, and confirm I am not pulling any legs.

The Code does not give any values for the freeboard, maybe this is because the freeboard may vary with width and flow, as in some other plumbing Codes. However I find that a value of about 60mm seems to work. This gives a water depth of 110 mm.

The total gutter depth, and rain water head dimensions are also plotted to the code sizes.

## As you can see, there is remarkable agreement with the Plumbing Code.

So we can all go away with a warm inner glow, knowing that a CFD simulation agrees with the Plumbing Code.

BTW my free programs also give the same results.

# Is this strange Logic?

When designing box gutters to the Australian Plumbing Code AS/NZS 3500 we design them for a once in 100 year storm event.

Now,  box gutters have always had a bad reputation for causing damage.  But with the advent of AS/NZS 3500 giving a concise method of designing box gutters, there should be no damage for all storms up to at least a 1 in 100 year event. (tested in the lab BTW)

Now the strange logic part. What if a hurricane or a cyclone, etc is taken as a 1 in 100 year storm event.

Our box gutter may be the least of our worries.

However just to protect one’s backside, in these days of  litigation etc. we should make sure our box gutters are designed for a once in 100 year storm. (Besides which it is mandatory under the code)

Just in case we get a wind free cyclone.

Alternatively, I hear you ask, what about the recent floods in Dungog? Surely that was a 1 in 100 year event?

They got a lot of rain there. But not much wind.

So, when your house is floating down the river, are you going to sue your Hydraulic Consultant if your box gutter springs a leak?

On second thought, yea probably, these days.

# Ever wondered what angle rain falls during a once in 100 year storm?

A 1 in 100 year storm could be a typhoon, a cyclone, a hurricane, or a tornado.

These storms have very strong winds, so what happens if the rain angle is actually horizontal?

If the rain was horizontal it wouldn’t hit the ground would it?  So does the rain just keep going until it eventually evaporates?

But that can’t be right because we have floods.

And if these events  are really once in 100 year storms, how come we can have one every year?

(refer to the comments below for the real answer). However continuing on for the rest of us….

The only logical answer is that the rain must come down somewhere, so once in every 100 years the rain comes down on your building.

At an angle of 63.4 degrees (2:1). Because that’s whats written in the Plumbing Code.

So it sort of takes it in turns, every 100 years your building is the lucky one, the structure at the end of the rainbow.

But not to worry, because if we use the plumbing code, we design all box gutters for this event.

We design for a 1 in 100 year storm with the  rain coming down at an angle of 63.4 degrees (2:1)

# HOW DOES ROOF SLOPE AFFECT THE CATCHMENT AREA?

The Plumbing Codes have a lot of stuff on this.

But for those of us who like to delve into things, and work out how things were derived. I will attempt to offer an explanation.

The crucial thing to understand is:-

Rainfall measurements are taken in inches or millimeters falling on a horizontal surface. The angle of the rain is not important. All that matters is the quantity of rain over a given area.

So when thinking about this, we need to calculate the area on a horizontal plane, where the rainfall would have fallen, if the roof wasn’t there. The roof intersects this amount of rainfall.

However to do this, somewhere along the line, someone has to dream up at what angle the rain is falling.

Fortunately for us, the powers that be have come up with an angle of 2:1 as shown in the diagram.

Just like anything to do with rainfall, there is no standard rainfall event. All we can do is base the design on averages, and figures pulled out of the air. For instance we design eaves gutters on a rainfall event that may, or may not, occur once in every 20 years. And a rainfall angle of 2:1 is as good as any, and in fact, as you will see later, this makes the calculations much easier.

Looking at the diagram, a roof from A to D also intersects the same amount of rain as the main roof.

In fact any roof between rainfall lines B and C, will intersect the same amount of rain, and therefore have the same catchment area.

But what is really interesting,  it doesn’t matter what the roof does to get from point A to point D. It can go up and down. or round and round. As long as the starting point is A, and the ending point is D, it will have the same catchment area.

Now, to determine what the real catchment area is, we must determine the area of the slope effect that must be added.

For a straight roof the Architect has normally shown this slope on the drawings. But if there are vertical drops, or different slopes we take the average as shown in the diagram. because this will intersect the same amount of rain.

Now the hard part, we have to do some mathematics.

We know the rain falls at an angle of 2:1, therefore in the diagram above, the length of the “slope effect added”, is half the “vertical rise” ( 2:1 remember). This is also true for the roof areas, that is, the area of the slope effect is half the area of the vertical rise, as both these lengths are multiplied by the same roof width to find the area.

So all we have to do now is find the area of the vertical rise. If you can remember your trigonometry, the vertical rise area = (roof plan area) * tan( roof slope).

Catchment area (CA)  = roof plan area + 1/2 (vertical rise area)

= roof plan area  +  1/2 *( roof plan area * tan (roof slope)

Ah, on second thoughts, its probably just as easy to look up the “slope factor” in the Plumbing Code, or simply measure the area from the Architects Elevations.

Any questions?

# What is a Rain Shadow? and why do I need to know?

When designing roof gutters, or surface drainage for building sites, The rain shadow can make a big difference. Especially for a tall building.

The Plumbing Codes assume rain is coming down at an angle of 2:1.

That is 2 units vertical to 1 unit horizontal. (63.4 degrees).

So from the diagram on the left, you can see the effect of the shadow.

The area of the shadow is half the area of the vertical face of the building. (2:1remember).

But what if rain comes from the other direction?

From the diagram on the right, you can see that half the vertical face of the building has been added to the catchment area.

The catchment area is always measured on the horizontal plane. Because that’s how they measure rainfall when they talk about ‘mm’ or ‘inches’ of rain.  So to make all our hydraulic formulas work, we must also use this method if we want to use rainfall figures calculated by the local Weather Bureau.

Now consider the interesting case where we have a building on both sides. One side has the shadow, and the other has the added catchment. If the buildings were of equal height, the effects would cancel each other out. No matter which direction the rain came from. Even if the rain came down the middle.

Got your head around that one yet?

However if the rain came from all directions at once, we are in diabolical trouble, and our roof gutter design, or site storm water design would be the least of our worries.