3. A vertical U-tube manometer is used to measure the pressure difference between and Ⓡ. However, the sensitivity of this measurement is less when his small (i.e. difficult to measure). Show by appropriate derivations with relevant parameters that the sensitivity can be improved (i.e. h can be higher for same difference between and ) if: a) The diameter of tube 2 is significantly lesser than that of tube 1. b) The tube 2 inclined at angle (0) with respect to the horizonal, Tube 1 where (0° < 0 < 90°) Both the criteria, a) and b) are met. c) e ↑ h Reference Fluid Tube 2

Fig: 1