convert following reading of pressure to kpa

Question

Convert following reading of pressure to kPa, supposing that the barometer reads 760mm Hg.

(1) 90cm Hg gauge
(2) 40cm Hg vacuum
(3) 1.2m H2O gauge

Sol: Given that h = 760mm of Hg for P_atm

P_atm =   gh = 13.6 × 103  × 9.81 × 760/1000 = 101396.16

N/m² = 101396.16Pa = 101.39KPa                                                                          ...(i)

(a)  90cm Hg gauge

P_gauge = gh = 13.6 × 103  × 9.81 × 90/100 = 120.07KPa                                             ...(ii)

P_abs  = P_atm  + P_gauge = 101.39 + 120.07

P_abs  = 221.46KPa                        .......ANS

(b)  40cm Hg vacuum

P_vacc =  gh = 13.6 × 103  × 9.81 × 40/100 = 53.366KPa                                           ...(iii)

P_abs  = P_atm  - P_vacc

= 101.39 - 53.366

P_abs  = 48.02KPa                           .......ANS

(c)1.2m Water gauge

P_gauge  =   gh = 1000 × 9.81 × 1.2 = 11.772KPa                                                              ...(iv)

P_abs  = P_atm  + P_gauge

= 101.39 + 11.772

P_abs  = 113.162KPa          .......ANS