## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

$P = P_0 + \rho~g~h$ where $P$ is the pressure $P_0$ is the atmospheric pressure $\rho$ is the density of the liquid $h$ is the depth below the surface We can find the height $h$ of the mercury when the gauge pressure at the bottom of the tube is 50 kPa. Therefore; $\rho~g~h = 50~kPa$ $h = \frac{50~kPa}{\rho~g}$ $h = \frac{5.0\times 10^4~N/m^2}{(13.6\times 10^3~kg/m^3)(9.80~m/s^2)}$ $h = 0.375~m = 37.5~cm$ The height of the tube is 37.5 cm.