Your company treats its wastewater by passing it through a filter before it is d

Question

Your company treats its wastewater by passing it through a filter before it is discharged. The filter consists of a 0.5 m-thick layer of coarse sand over a 1.5 m-thick layer of fine sand. Water enters the top of the filter, into the coarse sand. Water is maintained at a level 0.3 m above the top of the coarse sand (influent), and is discharged 0.2 m above the bottom of the fine sand (effluent). Both the influent and effluent are open to the atmosphere. The filter has a constant cross-sectional area of 5 m^2. The hydraulic conductivity of the coarse sand is 0.08 cm/s, and the water flowing through the filter has a density of 1 g/cm and a viscosity of 0.0125 g/(cm middot s). The filter is designed for a flow rate of 10.2 L/min. Lately, the flow rate has decreased to 1.8 L/min and you suspect that the fine sand layer has become partially plugged, decreasing its hydraulic conductivity. (a) What is the hydraulic conductivity of the partially-plugged fine sand layer, assuming the plugging is uniform throughout the fine sand and that the coarse sand is unaffected by the plugging? (b) How much higher is the water pressure (in Pa) at the top of the fine sand now compared to when the filter was operating at its designed flow rate? (c) A colleague proposes that the filter be redesigned so that the coarse sand is placed in a when the filter was operating at its designed flow rate? section that is 0.5 m thick with a cross-sectional area of 5 m^2 and a hydraulic conductivity of 0.08 cm/s, but that the fine sand is placed in a section that is 1.5 m thick with a cross- sectional area of 2 m^2 and a hydraulic conductivity of 0.003 cm/s. What would be the expected flow rate through this filter if the influent and effluent conditions remained the same as in parts (a) and (b)?

Explanation / Answer

a Ans

b Ans

As the height of level is maintained at 0.3 anbove the cource sand the pressure due to water in both the cases will be same.

But if we consider that eneregy of water drop at top surface is same in both cases we get

Pressure difference = change in KE of the drop

Difference in pressure is very low

C Ans

=36 L/min

Flow rate in Fine sand will be decinding factor so 36 L/min is expected

delta H    =    0.3+0.5+1.5-0.2 = 2.1 m delta L    =    0.5+1.5-0.2 = 1.8 m i = delta H/ delta L 1.167 A = 5 sqm Q = 1.8 L/min = 0.0018 m3/min k=Q/iA = 0.000308571 m/ min k= 0.00051 cm/sec

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