In one of the boiler rooms in an Industrial Plant, the barometer reads 750 mm Hg. Determine the absolute pressures in Kpa of the following pressure measuring instrument readings: pressure gauges reads 46 psi and 76 in. Hg; and compound gauges registers 13 Kpa vacuum and 2.5 psi vacuum.

To determine the absolute pressures in kPa, we need to convert the given pressure measurements from different units to a common unit.

First, let's convert the pressure gauge readings:

1. The pressure gauge reads 46 psi.
To convert psi to kPa, we can use the conversion factor: 1 psi = 6.89476 kPa.
So, to convert 46 psi to kPa, we multiply:
46 psi * 6.89476 kPa/psi = 317.39296 kPa (rounded to four decimal places).

2. The pressure gauge also reads 76 in. Hg (inches of mercury).
To convert in. Hg to kPa, we can use the conversion factor: 1 in. Hg = 3.38639 kPa.
So, to convert 76 in. Hg to kPa, we multiply:
76 in. Hg * 3.38639 kPa/in. Hg = 257.81364 kPa (rounded to four decimal places).

Next, let's convert the compound gauge readings:

1. The compound gauge registers 13 kPa vacuum.
To determine the absolute pressure, we need to add the atmospheric pressure (which is the pressure outside the system), which is typically 101.325 kPa.
Therefore, the absolute pressure is: 13 kPa + 101.325 kPa = 114.325 kPa (rounded to three decimal places).

2. The compound gauge also registers 2.5 psi vacuum.
To convert psi to kPa, we use the conversion factor: 1 psi = 6.89476 kPa.
To determine the absolute pressure, we add the atmospheric pressure (101.325 kPa) and subtract the vacuum pressure (2.5 psi * 6.89476 kPa/psi).
Therefore, the absolute pressure is: 101.325 kPa - (2.5 psi * 6.89476 kPa/psi) = 84.3781 kPa (rounded to four decimal places).

To summarize, the absolute pressures in kPa are as follows:
- Pressure gauge reading of 46 psi = 317.393 kPa.
- Pressure gauge reading of 76 in. Hg = 257.814 kPa.
- Compound gauge reading of 13 kPa vacuum = 114.325 kPa.
- Compound gauge reading of 2.5 psi vacuum = 84.3781 kPa.