# Flow through media

Practices which infiltrate surface runoff through an engineered soil or filter media, and discharge through an underdrain include stormwater planters and some forms of bioretention. The maximum flow rate from the BMP may be limited by the hydraulic conductivity of the medium, or by the properties of the perforated pipe.

The maximum flow rate through a bed of filter media (Qmax, media, m3/s) may be calculated as: ${\displaystyle Q_{max,media}={\frac {K_{m}\times A_{p}\times \left({\frac {h_{max}}{d_{m}}}\right)}{3.6\times 10^{6}}}}$

Where:

• Km is the hydraulic conductivity of the filter media (mm/hr),
• Ap is the area of the practice (m2),
• hmax is the total head of water within bioretention components over the perforated pipe (m) (i.e. ponding + mulch + filter media + choker layer), and
• dm is the depth of the filter media (m).

### Example calculations

A stormwater planter with footprint of 8 x 1.5 m is planned to receive runoff from an adjacent rooftop. The initial design for the planters includes 750 mm depth of filter medium, 50 mm rock mulch, and a further ponding of 300 mm. The underdrain pipe will be embedded into high performance bedding or similar, with a strip of geotextile over the top to prevent migration of the filter media into the pipe. The lab test states that the medium has a hydraulic conductivity of 25 mm/hr. The maximum flow through the medium is calculated and then a comparison made with the maximum flow through the pipe to see if the planter will drain freely: ${\displaystyle Q_{max,media}={\frac {25mm/hr\times 12\ m^{2}\times \left({\frac {1.1\ m}{0.75\ m}}\right)}{3.6\times 10^{6}}}=0.00012\ m^{3}/s}$

A bioretention cell with footprint of 30 x 10 m is planned to received runoff from adjacent roadways and parking facilities. The design includes 600 mm depth of filter medium, 75 mm wood based mulch, and ponding of 300 mm. Two underdrain pipes will be embedded at the base of the storage reservoir. These will connect together and then have an upturn within a manhole at the downstream end to prevent discharge until the head of water reaches the top of the storage reservoir within the cell. The lab test for the filter medium state that it has a hydraulic conductivity of 80 mm/hr. The downstream pipe in the manhole can convey 0.002 m3/s on a 1% slope.: ${\displaystyle Q_{max,media}={\frac {80mm/hr\times 300\ m^{2}\times \left({\frac {0.975\ m}{0.6\ m}}\right)\times 2}{3.6\times 10^{6}}}=0.0022\ m^{3}/s}$ As the maximum flow rate exceeds the downstream maximum permissible flow, the design must be amended. In order of preference, some options include:

1. Reformulating the bioretention filter media in collaboration with the soils provider, to reduce the hydraulic conductivity,
2. Reducing the depth of the filter media bed in agreement with a Landscape Architect, and increasing pretreatment (as filter bed < 600 mmm will provide less treatment),
3. Increasing the size of the downstream pipe to accommodate a greater flow rate.