Show that the derivative of an integral is given by

By generalizing to three dimensions show that the material derivative of an integral of a fluid property is given by

where the surface integral (∫_s) is over the surface bounding the volume v. Hence deduce that

Transcribed Image Text:

d dt -x2 (1) S x (t) x2 - [ of x1 p(x, t) dx = dx + dx p(x,t)- dt dx p(x,t). dt (P1.3)