Height required to attain backwash velocity (with headloss calculations)
After revising our siphon design a number of times, we came up the system shown above. We decided to build a basic model of this system, to see if the sizing and flow rates necessary are reasonable. We will determine both the relative height and volume of the clearwell. We based our model on a 55 gallon drum, a commodity known to be accessible and cheap in Honduras. We also decided to experiment with a well screen filter, that would sit at the interface between the sand and effluent pipe.
We have modeled this system in backwash mode to determine the necessary height difference between the clear-well and the bottom of the siphon.
We assembled the necessary equations in Mathcad using the relations below:
The sand bed pressure drop was modeled with the Carman Kozeny equation:
The pressure drop across the well screen was modeled with the orifice equation (for summation of holes):
The head loss across the piping and fittings was calculated using parameters from Morton M. Denn's Process Fluid Mechanics (page 93):
Viscous Losses due to fittings m2m^2/s2 s^2
Where ji is the "velocity heads lost" Coefficent, KfWe found the Velocity necessary to fluidize the bed from the empirical equation below:
For backwash velocity, we assume the rate of 1cm/second.