Answer to Question #284681 in Physics for John

Question

AU-tube of uniform cross-sectional area, open to the atmosphere, is partially filled with mercury. Water is then poured into both arms. If the equilibrium configuration of the tube is as

shown i*n_{j} with h_{2} = 2.5cr , determine the value of

h_{1}

Answer 1

The pressure in both arms must be the same:

$$\rho_\text{water}h_{\text{water left}}+\rho_mh_{m\text{ left}}=\\=\rho_\text{water}h_{\text{water right}}+\rho_mh_{m\text{ right}},\\\space\\ h_{m\text{ left}}=\dfrac{\rho_\text{water}h_{\text{water right}}}{\rho _m}+h_{m\text{ right}}.$$