$2\mathrm{.}59.$ The system shown in Fig. $2\mathrm{.}30$ is used to measure the density of a liquid in a tank. Compressed air or nitrogen flows at a very low rate through two dip tubes, whose ends are vertically $1\mathrm{.}00m$ apart. The difference in pressure between the two dip tubes is measured by a water manometer, which reads $1\mathrm{.}5m$ of water. The gas$-$flow rate is so slow that the gas in the dip tubes may be considered a static fluid. The density of the gas is $1\mathrm{.}21k\frac{g}{m^3}.$ What is the density of the fluid in the tank?

Two dip$-$tube density gauge.