Detention basin volumes
Detention basin storages can take many shapes, from natural landforms to shapes such as prisms and wedges. Volumes are calculated by taking horizontal 'slices' and calculating the volume of each slice by averaging the surface areas at the top and bottom of the slice and multiplying this by the depth of the slice.
Two formulae are commonly used - the end area method (averaging the areas of two 'slices' and multiplying by the difference in height between them) and the prismoidal formula, based on the formula below.
The prismoidal formula is considered to be generally superior and is used in DRAINS to calculate volumes from the surface areas defined in the Detention Basin property sheet. It is ideal for inverted cones, pyramids and other shapes which have constant sloping sides (going to a point) and for any shape with vertical walls. However, it can give erroneous results for some shapes, such as wedges, bowls and horizontal pipes (Wedges have constant sloping sides, but they go to a line - not a point. Bowls and horizontal pipes have curved side slopes). For such shapes the error, an under-estimate of volume, may be large if only two or three points are specified in the elevation-surface area storage. These errors can be reduced by specifying more surface areas at closer vertical spacings.
It is recommended that elevation-surface area relationships be established in a spreadsheet and pasted into the Detention Basin property sheet (using the Paste Table button). For wedge shapes at least eight surface area 'slices' should be specified to keep errors below 1%. If in doubt, conduct a test with a spreadsheet.
Some tools for calculating surface areas are included in the utility spreadsheet.
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