The troposphere power-law in a power series.
Whether the linear approximation
Explanation of Solution
Write the expression for the constant
Here, the acceleration due to gravity is
Write the equation of troposphere power-law.
Here, the pressure at some height is
Write the binominal equation.
Here, the variables are
Substitute
From equation (I), (II), and (III), write the troposphere power-law in a power series.
Write the ideal gas equation.
Here, the mass of the fluid is
Write the equation of the density.
Substitute
Substitute
Thus, the troposphere power-law in a power series is
For the linear law to be accurate the term
Since the starting point is not at zero so, substitute
Thus, the linear approximation
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Chapter 2 Solutions
Fluid Mechanics
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