1. Integral of a Vector Field over a Surface
Flux integrals

2. What is flux? Uniform fluid flow
Volume of fluid passing through surface in time interval Dt
Uniform fluid flow
“Field” = velocity of fluid at each point
Flat surface of area A, face on to flow
“Flux” = volume rate of flow

3. What is flux?
Volume of fluid passing through surface in time interval Dt
Uniform fluid flow
Flat surface of area A, tilted to flow

4. Why cos q ? Slice into thin horizontal disks and re-stack
Volume of right-angle cylinder
Slice into thin horizontal disks and re-stack
Slantwise cylinder

5. What is flux?
Volume of fluid passing through surface in time interval Dt
Uniform fluid flow
Flat surface of area A, tilted to flow
Flux through surface:

6. Sign of F

7. Non-uniform flow, curved surfaces