- #1

lorele

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## Homework Statement

A U-shaped tube of uniform section "S" has one extreme closed and the other one open to the atmosphere. The tube contains mercury (M) in the central part, a gas (G) to the left that exerts a pressure "p" and a column of water (W) of height [tex]h_w[/tex] to the right. Then, a mass "m" of another fluid of unknown density is poured over the right side and, when equilibrium is reached, the level of mercury on the left has risen "[itex]\Delta h[/itex]", and the pressure of G is now p'. Determine the increase of pressure p'-p of G according to the density of mercury ([itex]\rho_m[/itex]), [itex]\Delta h[/itex],

__S__and

__m__.

The given solution is

**[itex]p'-p={mg}/S - 2 \rho_m g \Delta h [/itex] .**

2. Homework Equations

2. Homework Equations

[tex]p=\rho g h[/tex]

## The Attempt at a Solution

krrk[tex]p'=p_{water} + p_{mercury} + p_{air}=\rho_w g h_w + \rho_m g h_{mercury} + p_{air} [/tex]

[tex]p=p_{water} + p'_{mercury} + p_{air} + p_{new}=

**\rho_w g h_w + \rho_m g (h_{mercury}+\Delta h) + p_{air} + {mg}/S [/tex]**

[tex]p'-p={mg}/S + \rho_m g \Delta h [/tex][/B]

[tex]p'-p={mg}/S + \rho_m g \Delta h [/tex]