Grantham Week 1 Discussion

If an equation is dimensionally correct, does this mean that the equation must be true? If an equation is not dimensionally correct, does this mean that the equation cannot be true? Explain.

Answer 1:

If an equation is dimensionally correct, it does not mean that the equation must be true. On the other hand, when the equation is dimensionally correct, the equation cannot be true.

Dimensional analysis is a technique used to check whether a relationship is correct. So, it can only tell you if a relationship is correct or not, but it can not tell you if it is completely right because of the numerics that may be involved in the calculations.

Answer 2:

An equation being dimensionally correct doesn’t mean that the equation is true. For instance, when calculating the area of a circle you can replace pi with another number and it would still be wrong while being dimensionally correct. However, if an equation is not dimensionally correct, the equation cannot be true. This is because if it is not dimensionally correct it would equate into something looking like 4 grapes = 4 bananas which could not happen.

Answer 3:

In order for an equation to be valid, the dimensions on the left side must match the dimensions on the right side, in which case it is dimensionally correct. An equation can be dimensionally correct but still can be wrong. However, if an equation is dimensionally incorrect, it must be wrong.

Answer 4:

No, a true equation must be dimensionally correct but some dimensionally correct equations are not true. Yes, unless the results of the equation produces the correct units, the equation cannot be correct.

Answer 5:

For an equation to be valid, the dimensions on the left side must match the dimensions on the right side (just like our oranges example.) It is then dimensionally correct.However an equation can be dimensionally correct but still wrong.
For example if I say the area of a circle = 2 x radius^2:
– this is dimensionally correct (both sides have dimensions L^2)
– but it is wrong, as ‘2’ should be ‘pi’.
On the other hand, if an equation is dimensionally incorrect, it must be wrong.

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