Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

Solutions
207

Since the mean pressure in the cabin remains un-
changed and equal to the atmospheric pressure Po,
the constant pi can be found from the condition
pal
Po= Pi + 2 '

where / is the length of the cabin. Thus, in the

middle of the cabin, the pressure is equal to the

atmospheric pressure, while in the front and rear

parts of the cabin, the pressure is lower and higher

than the atmospheric pressure by

pal ti

Op

2

0.03 Pa

respectively.

1.114. Let us consider the conditions of equilibri-

um for the mass of water contained between cross

sections separated by x and x Ax from the rota-

tional axis relative to the tube. This part of the

liquid, whose mass is pw S Ax, uniformly rotates at

an angular velocity w under the action of the forces

of pressure on its lateral surfaces. Denoting the

pressure in the section x by p (x), we obtain

[p (x Ax)— p (x)] S pS AVO 2 (x-j-

A

x

2 •

Making Ax tend to zero, we obtain the following

equation:

dp

dx =

w cox

whence

X^2

P (r) Pw(02 (-^2 — ) + Po.

Using the conditions of the problem

7. 2
   Pi= P

/ \

Pww 2 Po,

P2== P (r2) = Pww^2 + Po,