Question

mercury manometer is connected to open tank of fuel (Fig 8). Calculate a change of manometer readings

h if a level of fuel increases by ΔH. Take ΔH=0.2m, ρf=832 kg/m3, ρm=13600 kg/m3.

Answer 1

Solution;

Pressure on both sides of the arms of manometer should be equal.

The change in fuel level causes change is level of mercury and file in the manometer;

Pressure is give as ;

P=h$\rho$g

Equate;

$(\Delta H+\Delta h)\rho_{f}g=2\Delta h\rho_{m}g$

Divide both sides with g;

$(\Delta H+\Delta h)\rho_f=2\Delta h\rho_m$

Make $\Delta h$ the subject of formula;

$\Delta h=\frac{\Delta H×\rho_f}{(2\rho_m-\rho_f)}$ =$\frac{0.2×832}{(2×13600)-832}$

$\Delta h=0.006311m$

$\Delta h=0.6311cm$