Difficulty working with SI and derived SI conversions

[mpatryluk]

The physics textbook I'm working with doesn't seem to give me the required background for working with and understanding SI and derived units. Here is an example of something i am struggling with:

In studying fluid resistance, the book starts by displaying 2 equations.

1 is for fluid resistance when the object is at low speed and is f = kv (5.7)
The other is for when the object is at high speed and is f = Dv^2 (5.8)

In this case with the constants k and D my book has this to say:

You should verify that the units of the constant k in Eq. (5.7) are N x s/m or kg/s and that the units of the constant D in Eq. (5.8) are N x s^2/m^2 or kg/m

So the problem I'm having is that i see one of the two SI derived units (in bold) and i try to make sense of it intuitively. Like how a velocity = m/s, i can clearly imagine that it is the amount of metres traveled in a given length of time. But I have no idea where to start for intuition for these.

My thought process
For N x s/m, I read that as "Newton seconds per metre". So fiirstly, Newton-seconds: that's the amount of seconds for which a Newton force is applied? And then i try to conceptualize dividing that along a metre and i can't conceptualize it. Is it the quantity of Newton-seconds that "pass" in the travel of an object through one metre of fluid?
Edit: I thought i read that it was called dynamic viscosity, but on second inspection that would be m^2

Anyway, my general issue as evidenced above is my lack of certainty about how i should treat derived units: whether i should try to visualize them intuitively or what. Also which resources i could use to gain practice and understanding with working with these units.

 

[A.T.]

i should try to visualize them intuitively or what.

You can try, but it's not important. The units of constants are defined to make the equations work dimensionally.

- k tells you how many Newtons force increase per 1m/s velocity increase

- D tells you how many Newtons force increase per 1m^2/s^2 squared velocity increase (per area of a square with v as side length)

 

[Philip Wood]

Sorry if this seems like a patronising remark, but what a well-posed question, and what an excellent answer!

I think that looking for a the conceptual significance of units is good, but you've got to know when to give up and just treat a unit as a product of algebraic symbols! An example would be the unit of G in Newton's law of gravitation:
$$|\textbf F| = \frac{GMm}{r^2}.$$
If we leave the unit as $\text{N} \ \text{m}^{2} \ \text{kg}^{-2}$ it retains a manifest meaning. But if we express it in SI base units as $\text{kg}^{-1} \ \text{m}{^3} \ \text{s}^{-2}$ it's just a product of symbols. Still useful for checking homogeneity of units, of course.

Another nice example is $\mu_0$. Its SI units are N A^-2. You have to think about why m (metre) doesn't appear in the unit. I sometimes provocatively pronounce the unit "Newton per square ampère", but I suspect that's not relevant.