Chapter 3, Problem 58P

A U-tube manometer is used to measure the pressure in a vacuum chamber as shown in the sketch. The fluid in the vacuum chamber is of density ft, and the manometer fluid is of density ${\rho }_2$ . The right side of the U-tube manometer is exposed to atmospheric pressure P_atmand elevations $z_1,z_2$and $Z_A$ are measured.

a. Generate an exact expression for the vacuum pressure at point $A,i.e$ generate an expression for $P_{\text{A,vac}}$ as a function of variables ft. ${\rho }_1$ , ${\rho }_2,z_1,z_2$ and $z_A$
b. Simplify your expression for the case in which ${\rho }_1\ll {\rho }_2$ ,