Hydraulics of Rapid Sand Filtration
Methods and Materials
Figure 1: “Photograph of experimental apparatus for sand filtration.”
3 Figure 2. Flow Rate versus Bed Expansion
Bernoulli’s Equation: (1)
Darcy Weisbach Equation: (2)
Rose Equation: (3)
Expanded Bed Depth: (4)
Expanded Bed Porosity: (5)
Settling Velocity: (6)
Shape Factor: (7)
Table 1. Sand Properties
Table 2. Down Flow Data
Table 3. Up Flow Data
Table 4. Down Flow Analysis
Table 5. Up Flow Analysis
Rapid sand filters are used in water purification and municipal water treatment facilities. As water and suspended particles that were not removed during a prior treatment step are passed through filter media beds, the particles are removed by means of one or more mechanisms, leaving the water free of particulate matter and ready for final disinfection.
Water is pretreated using coagulants to flocculate the particles in the water. The particles clump together and the sand filters these clumps out of the water. The fine sand we used was between 0.38 mm and 0.8 mm. In a rapid sand filter water is introduced at the top of the tank and water filters through the anthracite coal and quartz sand and exits out of the bottom. As the sand comes in contact with the water it traps the particles and water flows through to the bottom. In normal operation they are set up for the media to be uniform and have consistent bed porosity. Rapid sand filters can deliver 150-200 million gallons of water per acre per day. They are designed to utilize the entire depth of a filter bed more fully to attain a higher throughput of water for a given surface area. The shape factor of the sand grains limits the filtration rate. High loading rates and deep penetration of solids into the beds limits the filtration rate and needs to be backwashed. Backwashing forces water up through the filter to fluidize and expand bed media. Cleansing occurs by scour cased by hydraulic shear forces and abrasion. The expanded media then settles after back washing. After the media settles it is ready to be used for filtration.
It is important to know the relationship between backwash rate and bed expansion to determine and appropriate backwash rate. Head loss is an important factor to help determine the backwash rate. Bernoulli’s equation is used to determine the head loss in a system (eqn. 1). Head loss in the sand filter system is mainly due to friction with the sand particles. Darcy Weishbach equation is used to predict the headloss for flow (eqn. 2). The Rose equation calculates the headloss for specific sand grains at varying flows (eqn. 3).
Darcy Weisbach Equation:
CD= drag coefficient, D=bed depth, g=gravity, v=velocity, d=diameter of avg sand grain, e=bed porosity, =shape factor coefficient (.73 for crushed sand, .83 for round sand, .75 for average sand)
The bed expansion depends on the backwash flow rate. As the backwash flow rate increases the bed will expand exponentially (eqn. 4). The expanded bed porosity from Equation 4 is a function of the backwash velocity and settling velocity of the individual sand grains (eqn. 5). The settling velocity can be calculated for the sand grains (eqn. 6).
Expanded Bed Depth:
De =expanded bed depth, D=packed bed depth, =porosity, =expanded bed porosity
Expanded Bed Porosity:
=expanded bed porosity, =backwash velocity, =settling velocity
Ss = specific gravity of sand, d = diameter of sand, CD = drag coefficient
4. Methods and Materials
A rapid sand column filter was employed that was 0.0318 ft (9.7cm) X 0.315 ft (9.6cm) X 1.48 ft (451.2cm) (Figure 1), which was filled with fine sand that had an average diameter of...
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