1. Basic mathematics
The scalar product of two vectors
and is a scalar.
Its value is:
. (1.1)
. (1.2)
The scalar product is commutative:
. (1.3)
The vectorial product of two vectors and is a vector perpendicular on the plane determined by those vectors, directed in such a manner that the trihedral , and should be rectangular.
. (1.4)
The modulus of the vectorial product is given by the relation:
. (1.5)
The vectorial product is non-commutative:
(1.6)
The mixed product of three vectors , and is a scalar.
. (1.7)
The double vectorial product of three vectors , and is a vector situated in the plane .
The formula of the double vectorial product:
. (1.8)
The operator is defined by:
. (1.9)
applied to a scalar is called gradient.
. (1.10)
scalary applied to a vector is called divarication.
. (1.11)
vectorially applied to a vector is called rotor.
. (1.12)
Operations with :
. (1.13)
. (1.14)
. (1.15)
When acts upon a product:
- in the first place has differential and only then vectorial proprieties;
- all the vectors or the scalars upon which it doesn’t act must, in the end, be placed in front of the operator;
- it mustn’t be placed alone at the end.
. (1.16)
. (1.17)
. (1.18)
, (1.19)
, (1.20)
, (1.21)
, (1.22)
. (1.23)
- the scalar considered constant,
- the scalar considered constant,
- the vector considered constant,
- the vector considered constant.
If:
(1.24)
then:
. (1.25)
The streamline is a curve tangent in each of its points to the velocity vector of the corresponding point .
The equation of the streamline is obtained by writing that the tangent to streamline is parallel to the vector velocity in its corresponding point:
Cursuri Mecanica fluidelor pt. cei de la navigatie si electromecanici. Curs in limba engleza
Documentul este oferit gratuit,
trebuie doar să te autentifici in contul tău.
