1) In 2011, the total of all residential customers in Halton Region used 54 540 000 m3 of water. Halton Region has a population of around 500 000 people and Milton (part of Halton Region) has a population of around 85 000 people. Assuming all people in Halton use the same amount of water, how much water was used in Milton in 2011?

V = 5.454e7m^3 ( 85000) = 9 271 800 m^3

2) 1 cm3 = 1 mL. The density of water is 1 g/cm3. Approximately what mass of water did Milton use in 2011?

mass = ρ(V) = 1000kg/m^3 ( 9.2718e6m^3) = 9.27e9 kg

3) Most houses in Milton draw their water from the municipal system that draws its water from Lake Ontario. Lake Ontario is 74 m above sea level and Milton is 221 m above sea level. The majority of the water in Milton passes through the water tower on Steeles Ave. It is 55 m from ground to top. In total, how much vertical distance must the water rise from Lake Ontario to the water tower?

202

4) How much gravitational potential energy does each kg of water gain travelling from Lake Ontario to the top of the water tower?

5) How much energy was needed to bring all the water used in Milton in 2011 from Lake Ontario to the water tower?

6) The energy used to lift the water comes from an electric water pump. Assuming the pump is 85% efficient at lifting the water, how much input electrical energy is needed for a year to lift the water?

7) Much of the energy used by the pump comes from natural gas fired plants (like the new one on Steeles Ave.). A typical efficiency for these power plants is 50%.
a. How much input energy (in the form of chemical energy) from natural gas is needed for a year to lift the water?

b. The chemical energy released from natural gas is around 35 MJ (Mega-Joules) per m3. What volume of gas needs to be burned to pump a year’s worth of water to Milton?

c. Use the internet to find the cost/m3 of natural gas in Ontario. Be sure to record your source. What is the cost to Milton to pump a year’s worth of water? Use the cost you think is appropriate.

See previous post: 5:29 PM.

4) To calculate the gravitational potential energy gained by each kg of water traveling from Lake Ontario to the top of the water tower, we can use the formula:

Gravitational Potential Energy (GPE) = mass × height × gravitational acceleration

Assuming the height from Lake Ontario to the water tower is the sum of the height of Milton (221 m), the height of the water tower (55 m), and the height of Lake Ontario (74 m), the total height is 221 m + 55 m + 74 m = 350 m.

Since the density of water is 1000 kg/m^3, the mass of each m^3 of water is 1000 kg. Therefore, the GPE gained by each m^3 of water is:

GPE = 1000 kg × 350 m × 9.8 m/s^2 = 3,430,000 J (Joules)

5) To calculate the total energy needed to bring all the water used in Milton in 2011 from Lake Ontario to the water tower, we need to multiply the energy gained per m^3 of water (3,430,000 J) by the total volume of water used in Milton in 2011 (9,271,800 m^3) from Question 1:

Total energy = GPE per m^3 of water × Total volume of water used in Milton

Total energy = 3,430,000 J/m^3 × 9,271,800 m^3 = 31,858,957,400,000 J (Joules)

6) Assuming the water pump is 85% efficient at lifting the water, we need to calculate the input electrical energy needed for a year to lift the water. Since energy efficiency is given by:

Efficiency = Useful output energy / Input energy

We can rearrange the equation to solve for the input energy:

Input energy = Useful output energy / Efficiency

Assuming the input energy is the same as the total energy calculated in Question 5, we have:

Input energy = Total energy / Efficiency

Input energy = 31,858,957,400,000 J / 0.85 = 37,541,124,000,000 J (Joules)

7a) To calculate the input energy (in the form of chemical energy) from natural gas needed for a year to lift the water, we need to understand the efficiency of the natural gas-fired plant. A typical efficiency for these power plants is 50%. Using the same efficiency equation as in Question 6:

Input energy from natural gas = Total energy / Efficiency

Input energy from natural gas = 31,858,957,400,000 J / 0.50 = 63,717,914,800,000 J (Joules)

b) The chemical energy released from natural gas is around 35 MJ (Mega-Joules) per m^3. To find the volume of gas needed to pump a year's worth of water to Milton, we divide the total energy needed by the energy per m^3:

Volume of gas = Total energy / Energy per m^3

Volume of gas = 31,858,957,400,000 J / (35 MJ/m^3 × 1,000,000 J/MJ) = 910,255.78 m^3

c) The cost of natural gas in Ontario varies, so you would need to check reliable sources such as utility company websites or government energy information websites to find the current cost per m^3 of natural gas.