7
for $y = f(x_1, ..., x_n)$, the sum of the partial differentials with respect to all of the independent variables is the total differential:
$$ dy = \frac{\partial y}{\partial x_1}dx_1+...+\frac{\partial y}{\partial x_n}dx_n $$
For our case:
$$ \dot{m} = \rho Av$$
$$ d\dot{m} = \frac{\partial \dot{m}}{\partial \rho}d\rho + \frac{\partial \dot{m}}{\partial A}...
3
the conservation of mass equation $ \dot m = \rho A V $ may be differentiated to obtain
$A V d\rho + \rho V dA + \rho A dV = 0 $
Which upon division by $ \rho A V $ yields
$ 0 = \frac{d\rho}{\rho} + \frac{dA}{A} + \frac{dV}{V}$.
The method for the first step is "partial derivatives". Explaining this method is outside the scope of the question I ...
1
According to New Atlas, a solar power plant went online in 2009. The principles are similar to your diagram, but simpler. Mirrors (not lenses) redirect sunlight to a single point atop a tower, which converts water to high pressure steam. The steam is used to spin turbine generators, located on-site. The expended steam is thereby cooled and condensed and used ...
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