How to size a box gutter for any flow by using the graphs in the Plumbing Code.

When designing Box Gutters, the graphs in the Australian Plumbing Code only allow for designs between the flows of 3L/s and 16L/s.

With industrial buildings getting bigger, there is a need to go outside these limits.

I will now show you how to do this by using those same graphs, and associated figures from the Plumbing Code AS/NZS 3500.3 2018

Step one: pick any size box gutter that fits on the relevant graph, and determine the depth, and the rain water head sizes.

Step two: Calculate the necessary scaling factor to scale the relevant dimension, for the flow you require.

However its not quite that easy. Scaling one dimension does not necessarily result in scaling another by the same amount.

For example, scaling the sides of a square by a factor of two, increases the area by a factor of 4.

Fluids are a bit like that. However there are things that can't be scaled, like gravity, viscosity, surface tension, friction etc.

So how do we find out the resultant scaling factor?

We start by finding an equation relevant to the situation that has all the related variables.

For box gutter depth, any equation incorporating flow, depth and width will do.

The best and simplest is the critical depth equation.

Critical depth occurs near the outfall of every box gutter.

The usual nomenclature applies Q = flow, W = width, Y = depth. Suffix 1 represents the base condition to be scaled, and suffix 2 the scaled result.

Critical depth formula

Try an Example

Assume our base gutter has Q1 = 5L/s, W1= 300, slope = 1:200, from Code fig I1 Box Gutter Depth1=110mm

Lets check for a new gutter with Q2=15L/s, W2 = 450, (any suitable width can be used), slope = 1:200. Multiplying factor:-

However a box gutter has a freeboard which we do not want to scale, So we take this value off the original BG depth, and add it back to the new BG depth (see below for how to calculate the freeboard)

So new BG depth =((orig depth - freeboard) x F ) + freeboard ...........(1)

= ((110 - 58) x 1.587) + 58

= 140 = Code Depth from fig I1 (for BG Q = 15 L/s, W = 450.)

How did we get the freeboard?

From fig I1 look up the BG depth for both gutters, and substitute in equation 1 above.

140 = ((110 - fb) x 1.587 ) + fb. solving, fb = 58mm

This does assume the new gutter depth will be the same as the code. However checking with all other Box Gutter combinations gives the same result.

So this value works in all situations.

RWH depth, scaling factor

Similarly we can find the scaling factor for the RWH depth from the orifice formula.

(for full derivation of the formula refer below)

RWH length, scaling factor

We can find the scaling factor for the RWH length from the trajectory formula

(for full derivation of the formula refer below)

Using this method, find the Box Gutter sizes for 150 L/s

Using a base gutter size of Q=10L/s, W=300, DP = 125, RWH D = 156, RWH L=158 

For Q=150L/s, Try width = 600, DP dia = 375,  results are as follows:-

Box gutter depth = 372, BG width = 600, RWH depth = 433, RWH Length = 470

But is this correct?

Failing a full size test, the next best thing is Computational Fluid Dynamics. (CFD)

The simulation at the top of the page was done using these dimensions, and the flow was checked by measuring the depth at the brink.

 The depth at the brink of a free outfall from a gutter = 0.7 x critical depth.

 As can be seen from the simulations, there is no overflowing.

Free Programs

If you don’t want to fool around with the graphs, you can get accurate interpolated results with these  Free Programs

However if you go above 16L/s these programs revert to formulas developed by the CSIRO, and require a small charge..

Once you have satisfied yourself that the theory works you can now:-

GO FORTH AND PROSPER 

For a full derivation of all formulas, Example calculations, and comparison with CSIRO formulas CLICK HERE

Ken Sutherland is a 'retired' (from design work) Hydraulic/civil Engineer who spent too much time analyzing the Plumbing Code and associated formulas. He now offers the benefit of this research and some of the resultant design programs, for free on the internet, for the benefit of the Construction industry, Architects, Engineers, Hydraulic consultants, students, and every other man and his dog.