Question

Convert the following readings of pressure to kPa assuming that barometer reads 760 mm of Hg. 

(i) 80 cm of Hg 

(ii) 30 cm Hg vacuum 

(iii) 1.35 m H₂O gauge 

(iv) 4.2 bar.

Answer 1

Assuming density of Hg, ρ_Hg = 13.596 × 1000 kg/m³ Pressure of 760 mm of Hg will be

= ρ × g × h = 13.596 × 1000 × 9.806 × \(\cfrac{760}{1000}\) 

(i) Pressure of 80 cm of Hg

= \(\cfrac{800}{760}\) x 101.325 = 106.65 kPa.

(ii) 30 cm Hg vacuum

= 76 – 30 = 46 cm of Hg absolute.

Pressure due to 46 cm of Hg

= \(\cfrac{460}{760}\) × 101.325 = 61.328 kPa. 

(iii) Pressure due to 1.35 m H₂O gauge

= 1000 × 9.806 × 1.35 = 13238 Pa = 13.238 kPa.

(iv) 4.2 bar

= 4.2 × 102 kPa = 420 kPa.

Note. Pressure of 1 atmosphere

= 760 mm of Hg 

or = 101325 N/m².

The above values are standard. To get this value we have to use ρ_Hg = 13596 kg/m³ and g = 9.806 m/s² . When we use ρ_Hg = 13600 kg/m³ and g = 9.81 m/s² , we get p_atm. = 101396 N/m² which is slightly different from 101325 N/m² . It is recommended that for pressure of 1 atm. the value 101325 N/m² should be used.