Question 5. Consider the equations of ideal gas dynamics (3.4)-(3.5) from Roberts (see the extracts from the book of Roberts on the Study Desk). Take = 7/5 (suitable for air) and find the distribution of density of an atmosphere in equilibrium when it is acted on by a uniform gravitational field F=-gp (assume p = po at z = 0). Sketch a graph of the density as a function of height z. This last equation supplies the third equation we need for the three unknowns: p, vand o. However, it is convenient to eliminate the stress o from the equations to give the two equations Әр at dz а +=(pv) = 0 др • (2² +10/²) = P-2²₂²-100. Ət dz (3.4) (3.5)
Question 5. Consider the equations of ideal gas dynamics (3.4)-(3.5) from Roberts (see the extracts from the book of Roberts on the Study Desk). Take = 7/5 (suitable for air) and find the distribution of density of an atmosphere in equilibrium when it is acted on by a uniform gravitational field F=-gp (assume p = po at z = 0). Sketch a graph of the density as a function of height z. This last equation supplies the third equation we need for the three unknowns: p, vand o. However, it is convenient to eliminate the stress o from the equations to give the two equations Әр at dz а +=(pv) = 0 др • (2² +10/²) = P-2²₂²-100. Ət dz (3.4) (3.5)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 5.
Consider the equations of ideal gas dynamics (3.4)-(3.5) from Roberts (see the
extracts from the book of Roberts on the Study Desk). Take y = 7/5 (suitable
for air) and find the distribution of density of an atmosphere in equilibrium
when it is acted on by a uniform gravitational field F=-gp (assume p = po at
z = 0). Sketch a graph of the density as a function of height z.
This last equation supplies the third equation we need for the three
unknowns: p, v and o. However, it is convenient to eliminate the stress
o from the equations to give the two equations
др, а
at 'дх
-(pv) = 0
dv
Ət
dr
for the two unknowns p and v.
+1
=
-k²pr-1
?х
(3.4)
(3.5)
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