Approximately Successfully
10 minutes and you’ll know if a project or product is feasible. A bold comment, but Ben Craven explained us the principles of approximate calculations. By using rough numbers and basic physics, the feasibility of a project can be planned out very quickly.
An example to demonstrate this principle?
Example 1: Could you gain energy by collecting rainwater from the roof of a building the size of the GSA Reid Building
I. Best or Worst Scenario?
If every value is assumed to be the best possible, and it still is not feasible in the end, we know for sure that it won’t be feasible.
In contrary, if every value is assumed to be the worst possible, and it is feasible, we know for sure that it will be feasible.
In this case we go for the Best Case Scenario:
Therefore, we assume the generator works with a 100% efficiency.
II. Approximate boundary conditions and constants
We have to identify the properties we need to know, to calculate the end result. These properties are the just roughly estimated or quickly looked up.
In this case we will need, the area of the roof, the height of the building and the rainfall per year in Glasgow.
With a quick internet search and very rough estimations, we agreed on following values:
Area = A = 75m*25m = 1875 m^2
Height = H = 40m
Average rainfall per year = 1.1m
III. Use basic physics
We then can start with to calculate, using basic Math and Physics.
Here we want to know the energy contained in the water falling down from the roof.
The potential energy P = m*g*h
Mass m = Volume*Density of Water = 1.1m*1875m^2*1000 kg/m3 = 2*10^6kg
Gravitational acceleration g = 9.81 m/s2
Height h = 40m
P=2*10^6kg*9.81 m/s^2* 40m = 75*10^8 J per year
IV. Quantify it
Sounds a lot, but how much is it actually? The calculated number has to be put into context now. Is it worth the money to install it? Answering the big questions, is it feasible or not?
Here we will try to find out how much energy would be produced per second and what we could roughly do with it.
In the moment we have energy per year, but we would like to have energy per second. So how many seconds are in a year?
1 year = 356 days* 24h*60min*60s = 31*106 s
75*10^8 J per year/31*10^6 s per year = 20 J/s = 20 W
20 W can roughly power 2 light bulbs. Not worth the effort – not feasible!
These 4 principles should be thought in first year of any engineering subject, if not even in any subject.
I. Best or Worst Scenario?
II. Approximate boundary conditions and constants
III. Use basic physics
IV. Quantify it
Using them could help you in any situation. It gives you a clear structure for critical thinking and understanding.
Any situation? Any situation:
Example 2: Food shopping
I. Best or Worst Scenario?
Worst scenario, I will get the most amount of food and everybody will be definitely fed
II. Approximate boundary conditions and constants
How many people, what’s the recipe?
III. Use basic physics
Multiply recipes quantities by the number of people coming
IV. Quantify it
Look at what you wrote down, divide it by the number of people and think, would I be full after that amount of food?
This is a stupid example, yes, but it also shows that we already use these principles in daily life. This is how we make decisions; this is how our brain plans.
So, why should we not use this for bigger decisions, bigger plans? Final Year Project????
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