irrotational vector वाक्य

उदाहरण वाक्य

1. In a simply connected open region, an irrotational vector field has the path-independence property.
2. In fluid dynamics, it is often referred to as a vortex-free or irrotational vector field.
3. For the test / weight functions one would choose the irrotational vector elements obtained from the gradient of the pressure element.
4. A closed vector field ( thought of as a 1-form ) is one whose derivative ( curl ) vanishes, and is called an irrotational vector field.
5. This can be seen by noting that in such a region, an irrotational vector field is conservative, and conservative vector fields have the path-independence property.
6. A generalization of this theorem is the Helmholtz decomposition which states that any vector field can be decomposed as a sum of a solenoidal vector field and an irrotational vector field.
7. Provided that U is simply connected, the converse of this is also true : Every irrotational vector field on U is a C ^ 1 conservative vector field on U.
8. The concepts of conservative and incompressible vector fields generalize to " n " dimensions, because gradient and divergence generalize to " n " dimensions; curl is defined only in three dimensions, thus the concept of irrotational vector field does not generalize in this way.
9. Because an irrotational vector field has a scalar potential and a solenoidal vector field has a vector potential, the Helmholtz decomposition states that a vector field ( satisfying appropriate smoothness and decay conditions ) can be decomposed as the sum of the form-\ operatorname { grad } \ Phi + \ operatorname { curl } \ mathbf { A } where is a scalar field, called scalar potential, and is a vector field called a vector potential.