Here is the question:
PLEASE DO NOT ANSWER THE QUESTION FOR ME!
A stream flows with velocity $\space q \space$. A wall is fixed in the stream and has normal $\space n \space$. Write down the (normal) boundary condition at the wall.
I love Mathematics A LOT as I can never use a formula or statement unless I know why it works.
I can often figure things out using what I already know, but sadly the one thing that stops me from doing that is the choice of words used.
I compliment the big vocabulary, but isn't there an easier, more obvious way to say things like the boundary condition?
It's not that I don't know what to do, I don't know what it's trying to ask me.
Yes, there are some words that can't necessarily be simplified any further. But some word problems just don't communicate well (at least to me). Despite my love for the subject.
I know it sounds dumb. But I'm a Mathematician, not an English graduate, master of the dictionary.
The principle of determinism in physics tells us that if we drop a massless bead in a velocity field (say, a river stream), the trajectory of the bead will be completely determined only if we specify the initial location of the bead. The movement of the bead is thought of as its position being a function of time, $p(t)$. The specification of $p(0)$ is called the initial condition, and its purpose is to give information about $p(t)$ at the point $t = 0$, which is a boundary point of the time domain $t \geq 0$.
Because the motion of a massless bead is specified by an ordinary differential equation of order $1$, only one piece of "boundary information" is needed. But, if the problem is to determine the shape of an elastic beam under some mechanical loads, the shape would depend on we do on each end of the beam: support it or clamp it. The endpoints of the beam are the boundary points of the domain, and a specification on what we do to the beam on each boundary point is a set of boundary conditions.
In your problem, the domain is: (the space in which your flow takes place) - (the barrier). The flow is found by solving a partial differential equation. But, the solution will be different, depending on what the flow is assumed to do at the boundary (i.e., depending on the boundary conditions).
The boundary conditions should reflect the physics of the phenomenon. A typical experimental observation for a flow around an obstacle is the "no-slip" condition: i.e., the components of the flow tangential to the boundary are zero. Or, if the barrier allows some partial seeping across the boundary (e.g., the barrier is porous), then this seeping is equal to the normal component of the flow: the flux across the boundary.
Not sure what your instructor intended here.
I would recommend checking out the two chapters on flow of water in Feynman's lectures in physics (the Flow of dry water and the Flow of wet water), and also seeing some examples in B. Bird's Transport Phenomena.