ABSTRACT
We give a brief account of the derivation of fundamental equations [3.1, 3.2]. We take a fluid volume V with its surface denoted by S, as in figure 3.1 ( n is the outward unit vector normal to S). For arbitrary V, we consider the temporal change of ∫ V η d V https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429148958/893f63fb-838b-43d9-9be3-ee81e9ce7f6a/content/eq14.tif"/> , where η represents a set of quantities per unit mass. The temporal change arises from the two effects as () ∂ ∂ t ∫ V η d V = ∫ S η ( − u n ) d S + S η . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429148958/893f63fb-838b-43d9-9be3-ee81e9ce7f6a/content/eq15.tif"/> Fluid volume for conservation laws. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429148958/893f63fb-838b-43d9-9be3-ee81e9ce7f6a/content/fig3_1.tif"/>
