Answer to Question #223793 in Physics for Alex Jordan

Question

The diagram shows a mercury manometer recording a pressure of 150 kPa. The atm pressure is 100 kPa. Density of mercury is 13600 kg m-3. What is the height difference h of the mercury surfaces?

Answer 1

We know that manometers measure absolute pressure, so, 150 kPa correspond to the pressure of

$$p_m=\rho gh_m,\\\space\\ h_m=\frac{p_m}{\rho g}.$$

Meanwhile the atmospheric pressure is

$$p_a=\rho gh_a,\\\space\\ h_a=\frac{p_a}{\rho g}.$$

The height difference h of the mercury surfaces:

$$h=h_m-h_a=\frac{1}{\rho g}(p_m-p_a),\\\space\\ h=\frac{1}{13600·9.8}(150000-10000)=0.38\text{ m}.$$