Expert: Daniel Mazur - 12/3/2008

Question
what is vector divided by scalar?is pressure scalar? is stress scalar

Answer
Hi Praneet,

A vector divided by a scalar is a vector. Pressure and stress are generally rank-two TENSORS and as you wrote no details, I don't know, at what level I should explain them to you. A simple depictive way is this:
scalar = one number
vector = one column or one row of N numbers (N-dimensional vector)
tensor rank-two = a table of N rows and M columns
tensor rank-three = a stack of tables of N rows, M columns and L layers
e.t.c.

In fact the general mathematical structure is "tensor". Subsequently, vectors can be called "rank-one tensors" and scalars are "rank-zero tensors". Nevertheless, these expressions are rarely used, because scalars and vectors have certain special properties. They are also more useful at the high-school level, and only tiny minority of people ever studies maths (and hence tensors) at a university.

Back to your question: pressure and stress are generally rank-2 tensors. However, if the pressed and stressed material is homogeneous and isotropic (many materials are at least approximately so), then all numbers in the tensors are the same, which means that SCALARS of the same value can be used instead. In case you need this for a high-school class, then you probably will need to come up with the answer: "Pressure and stress are scalars for homogeneous and isotropic materials." The other option (vector) is definitely wrong.

Cheers,
Daniel