Fundamental Definition
Volume flow rate is defined by the limit:
I.e., the flow of volume of fluid V through a surface per unit time t.
Since this is only the time derivative of volume, a scalar quantity, the volumetric flow rate is also a scalar quantity. The change in volume is the amount that flows after crossing the boundary for some time duration, not simply the initial amount of volume at the boundary minus the final amount at the boundary, since the change in volume flowing through the area would be zero for steady flow (which isn't the case, since an amount of volume has passed the boundary in the time duration).
Read more about this topic: Volumetric Flow Rate
Famous quotes containing the words fundamental and/or definition:
“This is the fundamental idea of culture, insofar as it sets but one task for each of us: to further the production of the philosopher, of the artist, and of the saint within us and outside us, and thereby to work at the consummation of nature.”
—Friedrich Nietzsche (18441900)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on life (based on wording in the First Edition, 1935)