Physics Portion

Gabriel and Alec do a Physics Investigation

Design

Research Question:

How does time affect the flow rate of water Q through a gravity-fed sand filtration system?

Hypothesis:

The original hypothesis of the experiment was that flow rate will gradually decrease as time increases.

Variables:

The independent variable in the investigation is time in seconds of filtration, and the dependent variable is flow rate of the system Q in mL/s.

Controlled variables include the type and amount of sand and gravel used in the filtration system, the water used, and the filtration system used.

●The type and amount of sand and gravel was controlled by using the same materials throughout the experiment.

●The type of water used in the experiment was controlled by using a solution of tap water and baking soda of a specific quantity (see Chemistry Portion)

●The filtration system itself was maintained to be the same throughout the experiment (see System Design)

Materials:

• 1 5/8" diameter PVC tube at least 40 cm long
• 1 5/8" PVC plug
• 1cm diameter plastic tubing
• 500mL collection beaker
• Funnel
• Fine Sand
• Coarse gravel
• One coffee filter
• Two Milli-Pore filters (0.02m radius)
• 1L Tap Water 0.5 M Sodium Bicarbonate
• Stopwatch

System Design and Procedure

System Design:

1. The plug is placed in the PVC tube and sealed with a glue to make it watertight.
2. A small hole is drilled in the PVC tube to fit the plastic tubing. The plastic tube should be inserted in the pipe and be watertight.
3. The PVC tube is filled with 323.3 g of coarse gravel on the bottom.
4. 3 millipore filters cut to fit the diameter of the tube (0.02 m) and one coffee filter are placed in the pipe over the gravel. (These filters are to filter excess sand. They do not filter the solution.)
5. 268.0 g of fine sand are placed on top of the coffee filter.

Experimental Procedure:

1. 310 mL of baking soda solution are poured into the funnel and pipe and the stopwatch is started
2. As the water saturates the filter and begins to flow through the pipe volumes of water in the collection beaker are recorded every 30 seconds
3. This 30 second interval is repeated until water flow from the pipe is negligible

Data Collection and Processing

Using the stopwatch and collection beaker, the amount of total solution filtered was recorded at regular intervals of 30 seconds. The first 90 seconds record no solution filtered as the sand was not yet saturated to the point that the solution would flow through it.

Time (s)	Solution Filtered (mL)
30	0
60	0
90	0
120	10
150	25
180	55
210	70
240	80
270	90
300	100
330	110
360	125
390	140
420	150
450	160
480	170
510	180
540	185
570	195
600	200
630	200
660	205
690	210
720	210
750	210

This data represents the total volume of water collected. The aim of the experiment is to track flow rate Q, which can be expressed by: (where V represents volume and t represents time)

Q=dV/dt

This average will be calculated by dividing the change in volume for each interval by the change in time, 30 seconds. For example, the average flow rate for the interval from 120 seconds to 150 seconds is:

Because this is an average from 120 to 150 seconds, it will be recorded as 135 seconds. All of the Processed Data, then, appears:

Time (s)	Average Flow Rate (mL/s)
15	0
45	0
75	0
105	0.3
135	0.5
165	1
195	0.5
225	0.3
255	0.3
285	0.3
315	0.3
345	0.5
375	0.5
405	0.3
435	0.3
465	0.3
495	0.3
525	0.2
555	0.3
585	0.2
615	0
645	0.2
675	0.2
705	0
735	0

Using plotting software, this data appears:

The software suggests that the data is fitted best by the trendline:

Q = -2E-11t4 + 5E-08t3 - 3E-05t2 + 0.0083t - 0.2237

Conclusion and Evaluation

The trendline appears to support the experiment’s original hypothesis that as time increases the flow rate of the filtration system will decrease. This is, of course, because the supply of water was poured in once rather than being kept steady over time. Regardless, the results are not very accurate and as such the trend line fits through very few data points. This could be improved by taking both more measurements and recording the volume of water filtered to a higher degree of accuracy. It would also be helpful to test how the amount of solution put into the filter affects the total time for filtration or to run more trials for the current amount of solution to record more accurate data.

The experiment in relation to the other subject areas would benefit from any number of other improvements, many of which center around the filter’s inability to actually filter particulate matter (see Chemistry.) After comparing this filtration system to industrial sand filtration systems, it seems that our system would have to work much slower and use much more sand to properly filter the solution.

Ultimately, this information for flow rate has many real-world applications. Using this system as a basis for extrapolation (and a maximum flow rate of approximately 0.5mL/s) it can be estimated how quickly a similar system could filter water, or how long the system would take to filter a fixed quantity of water. The system would need further testing and improvement before it is scaled up, of course. Some questions that stem from the experiment which may be explored still include:

• What experimental setup minimizes the escape of particulate matter?
• What has a greater effect on flow rate: the volume of sand in the pipe or the height of the sand which the water must filter through first?
• Does the density of the sand affect the flow rate of the system?
• What is the optimized balance between filtration effectiveness and flow rate?

Physics!

Alec cleaning a filter

Gabriel pouring a solution into the filter

Alec working with his cat while sick to bed with pneumonia

An initial test run and some muddy results