For an example of applications of surface integrals, consider a vector field on a surface ; that is, for each point in , is a vector. Imagine that a fluid flows through , such that determines the velocity of the fluid at . The flux is defined as the quantity of fluid flowing through in unit amount of time. To find the flux, one need to take the dot product of with the unit surface normal to at each point, which will give a scalar field, which is integrated over the surface: