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?
See previous post: 5:29 PM.
4) The gravitational potential energy gained by each kg of water traveling from Lake Ontario to the top of the water tower can be calculated using the formula:
Potential Energy = mass * acceleration due to gravity * height
Assuming a height difference of 166 meters (221 - 55), the potential energy gained by each kg of water is:
Potential Energy = 1 kg * 9.8 m/s^2 * 166 m = 1626.8 J
5) To calculate the total energy needed to bring all the water used in Milton from Lake Ontario to the water tower, we can multiply the mass of water used in Milton (9.27e9 kg) by the potential energy gained per kg of water (1626.8 J):
Total Energy = mass of water * potential energy gained per kg of water
Total Energy = 9.27e9 kg * 1626.8 J = 1.51e13 J
6) Since the pump is 85% efficient, we need to calculate the input electrical energy needed to lift the water by dividing the total energy by the efficiency:
Input Electrical Energy = Total Energy / Efficiency
Input Electrical Energy = 1.51e13 J / 0.85 = 1.78e13 J
7a) To calculate the input energy in the form of chemical energy needed from natural gas, we divide the input electrical energy by the efficiency of the power plant:
Input Chemical Energy = Input Electrical Energy / Efficiency of power plant
Input Chemical Energy = 1.78e13 J / 0.5 = 3.56e13 J
b) To determine the volume of natural gas needed to pump a year's worth of water to Milton, we divide the input chemical energy by the energy released per m3 of natural gas:
Volume of gas = Input Chemical Energy / Energy released per m3 of natural gas
Volume of gas = 3.56e13 J / 35 MJ = 1.02e9 m3
Therefore, approximately 1.02 billion m3 of natural gas needs to be burned to pump a year's worth of water to Milton.
To determine the answers to these questions, we need to go step by step and calculate each value accordingly. Let's break it down:
2) To find the mass of water used in Milton, you can multiply the volume of water used (9,271,800 m3) by the density of water (1 g/cm3 or 1000 kg/m3).
Mass = Density x Volume
Mass = 1000 kg/m^3 x 9,271,800 m^3
Mass = 9.27 x 10^9 kg
3) The vertical distance the water needs to rise from Lake Ontario to the water tower is the difference in elevation between the two points.
Elevation difference = 221 m - 74 m = 147 m
4) To calculate the gravitational potential energy gained by each kg of water, you can use the formula:
Gravitational Potential Energy = Mass x Acceleration due to gravity x Height
Gravitational Potential Energy = 1 kg x 9.8 m/s^2 x 147 m
Gravitational Potential Energy = 1438.2 Joules
5) To find the total energy needed to bring all the water from Lake Ontario to the water tower, you can multiply the gravitational potential energy gained by each kg of water (1438.2 J) by the total mass of water used in Milton (9.27 x 10^9 kg).
Total Energy = Gravitational Potential Energy x Mass
Total Energy = 1438.2 J/kg x 9.27 x 10^9 kg
Total Energy = 1.335 x 10^13 Joules
6) Assuming the pump is 85% efficient, the input electrical energy needed to lift the water can be calculated by dividing the total energy required (1.335 x 10^13 J) by the efficiency (0.85).
Input Electrical Energy = Total Energy / Efficiency
Input Electrical Energy = 1.335 x 10^13 J / 0.85
Input Electrical Energy = 1.57 x 10^13 Joules
7a) As mentioned, the power plants' efficiency is 50%, meaning that only half of the chemical energy from natural gas is converted into electrical energy.
Input Chemical Energy (Natural Gas) = Input Electrical Energy / Efficiency
Input Chemical Energy (Natural Gas) = 1.57 x 10^13 J / 0.5
Input Chemical Energy (Natural Gas) = 3.14 x 10^13 Joules
7b) Given that the chemical energy released from natural gas is 35 MJ/m3, we can calculate the volume of gas needed to pump a year's worth of water.
Volume of Gas = Input Chemical Energy (Natural Gas) / Energy Released per m3
Volume of Gas = 3.14 x 10^13 J / 35 x 10^6 J/m3
Volume of Gas = 8.97 x 10^5 m3
By following these calculations, you can find the answers to each question.