Question

Determine the head loss during backwash for a filter bed consisting of 0.6 m of sand with f = 0.45, 0.4 m gravel, and a pipe lateral under drain with a circular orifice having α = 0.8 and β = 0.05, Vb = 0.8 m/min.

Answer 1

The head loss during backwash for this filter bed is:

HL = (3.70ρVb2)/(2g[αf + β])

where ρ = density of the fluid (typically water), Vb = backwash velocity, g = acceleration due to gravity, α = orifice discharge coefficient, f = bed porosity, and β = orifice area ratio (orifice area / pipe lateral area).

For the given filter bed, the head loss is equal to:

HL = (3.70*1000*(0.8 m/min)^2)/(2*9.81*(0.8*0.45 + 0.05)) = 0.124m

The head loss during backwash is mostly due to friction loss as the water flows through the filter bed and friction loss is caused by the resistance to flow of the bed particles. The orifice is also a source of head loss due to the sudden expansion of the water from the pipe lateral to the orifice.