// Numbas version: finer_feedback_settings {"name": "Water Treatment Practical - 2025 ", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "WTA - Test - Final", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sahish Bhosle", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/27950/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

\"Water Treatment Practical\"

Mission:

Your task is to help a community of 10,000 people by designing an affordable, efficient water treatment system!

Instructions:

The assessment is not marked, but each question has a scoring system to indicate correctness. Only proceed to the next question if you achieve full marks on the current one.

Ensure everyone contributes to the discussion.
You may consult lecture materials or use online resources for unit conversions.
Hints are available—use them if you're stuck, but try solving each step independently first!

Please click on the 'End Exam' button once you are done!

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"data_info": {"name": "data_info", "group": "Ungrouped variables", "definition": "safe(\"

Hint:

\\n

Multiply your volume in mL by 0.000001.

\")", "description": "", "templateType": "long string", "can_override": false}, "volume_1": {"name": "volume_1", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "data_info1": {"name": "data_info1", "group": "Ungrouped variables", "definition": "safe(\"

Hint: To convert seconds into hours, divide the time in seconds by 3600 (since there are 3600 seconds in an hour).

\")", "description": "", "templateType": "long string", "can_override": false}, "data_info2": {"name": "data_info2", "group": "Ungrouped variables", "definition": "safe(\"

Hint: The Surface area of a circle is calculated using the formula [ πr²=3.14×(Radius)²]

\")", "description": "", "templateType": "long string", "can_override": false}, "sur_area": {"name": "sur_area", "group": "Ungrouped variables", "definition": "0.79", "description": "", "templateType": "anything", "can_override": false}, "data_info3": {"name": "data_info3", "group": "Ungrouped variables", "definition": "safe(\"

Hint: Remember to convert cm² to m²! 1 cm² = 0.0001 m².

\")", "description": "", "templateType": "long string", "can_override": false}, "sur_aream2": {"name": "sur_aream2", "group": "Ungrouped variables", "definition": "sur_area*0.0001", "description": "", "templateType": "anything", "can_override": false}, "data_info4": {"name": "data_info4", "group": "Ungrouped variables", "definition": "safe(\"

Formula:

\\n

$\\\\text{Filtration rate (m/hr)} = \\\\frac{\\\\text{Water volume (m³)}}{\\\\text{Time (hr)} \\\\times \\\\text{Surface area (m²)}}$

\")", "description": "", "templateType": "long string", "can_override": false}, "water_quantity": {"name": "water_quantity", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "water_quantitym3": {"name": "water_quantitym3", "group": "Ungrouped variables", "definition": "water_quantity/1000.0", "description": "", "templateType": "anything", "can_override": false}, "water_quantityhr": {"name": "water_quantityhr", "group": "Ungrouped variables", "definition": "water_quantitym3/24.0", "description": "", "templateType": "anything", "can_override": false}, "data_info5": {"name": "data_info5", "group": "Ungrouped variables", "definition": "safe(\"

Now let\\'s calculate the surface area of the tank required for each trial using this formula:

\\n

$\\\\text{Surface area (m²)} = \\\\frac{\\\\text{Volume of water treated (m³/hr)}}{\\\\text{Filtration rate (m/hr)}}$

\\n

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Now lets calulate the surface area of the tank you entered before required for each trial using this formula:

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"templateType": "anything", "can_override": false}, "tank_gravel_volume2": {"name": "tank_gravel_volume2", "group": "Ungrouped variables", "definition": "tank_gravel_depth2*length2*width2", "description": "", "templateType": "anything", "can_override": false}, "tank_gravel_volume3": {"name": "tank_gravel_volume3", "group": "Ungrouped variables", "definition": "tank_gravel_depth3*length3*width3", "description": "", "templateType": "anything", "can_override": false}, "tank_ac_volume1": {"name": "tank_ac_volume1", "group": "Ungrouped variables", "definition": "tank_ac_depth1*length1*width1", "description": "", "templateType": "anything", "can_override": false}, "tank_ac_volume2": {"name": "tank_ac_volume2", "group": "Ungrouped variables", "definition": "tank_ac_depth2*length2*width2", "description": "", "templateType": "anything", "can_override": false}, "tank_ac_volume3": {"name": "tank_ac_volume3", "group": "Ungrouped variables", "definition": "tank_ac_depth3*length3*width3", "description": "", "templateType": "anything", "can_override": false}, "cost_gravel1": {"name": "cost_gravel1", "group": "Ungrouped variables", "definition": "tank_gravel_volume1*30", "description": "", "templateType": "anything", "can_override": false}, "cost_sand1": {"name": "cost_sand1", "group": "Ungrouped variables", "definition": "tank_sand_volume1*50", "description": "", "templateType": "anything", "can_override": false}, "cost_ac1": {"name": "cost_ac1", "group": "Ungrouped variables", "definition": "tank_ac_volume1*100", "description": "", "templateType": "anything", "can_override": false}, "cost_sand2": {"name": "cost_sand2", "group": "Ungrouped variables", "definition": "tank_sand_volume2*50", "description": "", "templateType": "anything", "can_override": false}, "cost_gravel2": {"name": "cost_gravel2", "group": "Ungrouped variables", "definition": "tank_gravel_volume2*30", "description": "", "templateType": "anything", "can_override": false}, "cost_ac2": {"name": "cost_ac2", "group": "Ungrouped variables", "definition": "tank_ac_volume2*100", "description": "", "templateType": "anything", "can_override": false}, "cost_gravel3": {"name": "cost_gravel3", "group": "Ungrouped variables", "definition": "tank_gravel_volume3*30", "description": "", "templateType": "anything", "can_override": false}, "cost_sand3": {"name": "cost_sand3", "group": "Ungrouped variables", "definition": "tank_sand_volume3*50", "description": "", "templateType": "anything", "can_override": false}, "cost_ac3": {"name": "cost_ac3", "group": "Ungrouped variables", "definition": "tank_ac_volume3*100", "description": "", "templateType": "anything", "can_override": false}, "total_cost1": {"name": "total_cost1", "group": "Ungrouped variables", "definition": "cost_sand1+cost_gravel1+cost_ac1", "description": "", "templateType": "anything", "can_override": false}, "total_cost2": {"name": "total_cost2", "group": "Ungrouped variables", "definition": "cost_sand2+cost_gravel2+cost_ac2", "description": "", "templateType": "anything", "can_override": false}, "total_cost3": {"name": "total_cost3", "group": "Ungrouped variables", "definition": "cost_sand3+cost_gravel3+cost_ac3", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["volume_1", "data_info", "data_info3", "data_info1", "data_info2", "sur_area", "sur_aream2", "data_info4", "water_quantity", "water_quantitym3", "water_quantityhr", "data_info5", "volume_2", "volume_3", "volume_1m3", "volume_2m3", "volume_3m3", "time_1", "time_2", "time_3", "time_1hr", "time_2hr", "time_3hr", "filter_1", "filter_2", "filter_3", "sa_1", "sa_2", "sa_3", "length1", "width1", "width2", "width3", "length2", "length3", "data_info6", "sand_depth1", "sand_depth2", "sand_depth3", "gravel_depth1", "gravel_depth2", "gravel_depth3", "ac_depth1", "ac_depth2", "ac_depth3", "tank_sand_depth1", "tank_sand_depth2", "tank_sand_depth3", "tank_gravel_depth1", "tank_gravel_depth2", "tank_gravel_depth3", "tank_ac_depth1", "tank_ac_depth2", "tank_ac_depth3", "tank_sand_volume1", "tank_sand_volume2", "tank_sand_volume3", "tank_gravel_volume1", "tank_gravel_volume2", "tank_gravel_volume3", "tank_ac_volume1", "tank_ac_volume2", "tank_ac_volume3", "cost_gravel1", "cost_sand1", "cost_ac1", "cost_sand2", "cost_gravel2", "cost_ac2", "cost_gravel3", "cost_sand3", "cost_ac3", "total_cost1", "total_cost2", "total_cost3"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": true, "customName": "Part 1: Filtration Rate", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

You filtered water through a small glass tube and measured the time it took for the water to pass through. Now, you will use the following steps to calculate the filtration rate.

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For each of the three trials, enter the volume of the water filtered:

Volume filtered in Trial 1: [[0]] mL

Volume filtered in Trial 2: [[1]] mL

Volume filtered in Trial 3: [[2]] mL

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Now convert the volume of the water filtered in m³:

{data_info}

Volume filtered in Trial 1: [[0]] m³

Volume filtered in Trial 2: [[1]] m³

Volume filtered in Trial 3: [[2]] m³

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How long did it take for the water to filter in each of the three trials?

Time Taken for Trial 1: [[0]] seconds

Time Taken for Trial 2: [[1]] seconds

Time Taken for Trial 3: [[2]] seconds

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Now convert the time to hours for each of the three trials:

{data_info1}

Time Taken for Trial 1: [[0]] hours

Time Taken for Trial 2: [[1]] hours

Time Taken for Trial 3: [[2]] hours

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Calculate the surface area of the tube?.

We filtered water through a glass tube. Let’s calculate its surface area step-by-step. (The radius of the glass tube used is 0.5 cm.)

{data_info2}

Surface Area: [[0]] cm²

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Convert the surface area to m²

{data_info3}

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We’re now finally ready to calculate how fast the water flowed through the filter in all three trials!

{data_info4}

Filtration rate for Trial 1: [[0]] m/hr

Filtration rate for Trial 2: [[1]] m/hr

Filtration rate for Trial 3: [[2]] m/hr

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It’s time to scale up your design to help a town of 10,000 people.

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Each person uses 150 L/day.

What is the total quantity of water needed per day for 10000 people?

Water Quantity: [[0]] L

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Now convert the volume to m³

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What is the volume of water needed per hour? (m³/hr)

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{data_info5}

Calculate the surface area of the tank for each of the three trials?

Surface Area for Trial 1: [[0]] m²

Surface Area for Trial 2: [[1]] m²

Surface Area for Trial 3: [[2]] m²

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It's time to design your tank! To ensure it works, the Length × Width must be at least equal to the Tank Surface Area you calculated earlier—but not excessively large. A tank that is too small won’t treat enough water, while a tank that is too large will be expensive to build. Aim for balance!

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Design your tank assuming it’s 1 m deep:

For Trial 1:

Length of the proposed tank: [[0]] m

Width of the proposed tank: [[1]] m

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Verification Step: Surface Area of the Tank for Trial 1

If the calculated surface area is not correct (not equal to or within 10% of the required value), go back and revise the Length and Width values for Trial 1.

Note: The surface area for the dimensions you enter must match the required surface area or be at most 10% greater.

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Design your tank assuming it’s 1 m deep:

For Trial 2:

Length of the proposed tank: [[0]] m

Width of the proposed tank: [[1]] m

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Verification Step: Surface Area of the Tank for Trial 2

If the calculated surface area is not correct (not equal to or within 10% of the required value), go back and revise the Length and Width values for Trial 2.

Note: The surface area for the dimensions you enter must match the required surface area or be at most 10% greater.

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Design your tank assuming it’s 1 m deep:

For Trial 3:

Length of the proposed tank: [[0]] m

Width of the proposed tank: [[1]] m

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Verification Step: Surface Area of the Tank for Trial 3

If the calculated surface area is not correct (not equal to or within 10% of the required value), go back and revise the Length and Width values for Trial 3.

Note: The surface area for the dimensions you enter must match the required surface area or be at most 10% greater.

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Calculate the cost of your tank based on the materials used.

Material Costs:

Sand = £50/m³
Gravel = £30/m³
Activated Carbon = £100/m³

Remember that the tank depth is fixed at 1m. Since your small-scale experiment used a 10 cm (0.1 m) deep filter, you need to scale up each material depth by a factor of 10 to match the full-scale tank depth. For length and width use the values you proposed in the previous step.

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For Trial 1:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Material	Material Cost	Depth of the Material in the cylinder (cm)	Material Depth - Scaled up (S) (m)	\n Total volume of the Material in the tank (m³) = \n S x Width x Length \n	Cost (£)	Turbidity
Sand	50	[[0]]	[[9]]	[[18]]	[[27]]
Gravel	30	[[3]]	[[12]]	[[21]]	[[30]]
Activated Carbon	100	[[6]]	[[15]]	[[24]]	[[33]]
Total					\n [[36]] \n	\n [[39]] \n

For Trial 2:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Material	Material Cost	Depth of the Material in the cylinder (cm)	Material Depth - Scaled up (S) (m)	\n Total volume of the Material in the tank (m³) = \n S x Width x Length \n	Cost (£)	Turbidity
Sand	50	[[1]]	[[10]]	[[19]]	[[28]]
Gravel	30	[[4]]	[[13]]	[[22]]	[[31]]
Activated Carbon	100	[[7]]	[[16]]	[[25]]	[[34]]
Total					\n [[37]] \n	\n [[40]] \n

For Trial 3:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Material	Material Cost	Depth of the Material in the cylinder (cm)	Material Depth - Scaled up (S) (m)	\n Total volume of the Material in the tank (m³) = \n S x Width x Length \n	Cost (£)	Turbidity
Sand	50	[[2]]	[[11]]	[[20]]	[[29]]
Gravel	30	[[5]]	[[14]]	[[23]]	[[32]]
Activated Carbon	100	[[8]]	[[17]]	[[26]]	[[35]]
Total					\n [[38]] \n	\n [[41]] \n

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