Question

The absolute pressure inside the cylinder is now 500 kPa. Ifa gauge were used to measure the gauge pressure inside the system in mm of mercury, what would it be? Assume pmercury = 13595 kg/m3 and g = 9.80665 m/s2

Answer 1

Gauge pressure = 2990.32 mmHg

Step-by-step explanation:

Step 1

Calculation of Gauge Pressure

Gauge pressure = Absolute pressure - Atmospheric pressure

Absolute pressure = 500 kPa = 500000 Pa

Atmospheric pressure = 101325 Pa

Gauge pressure = Absolute pressure - Atmospheric pressure

= 500000 - 101325

= 398675 Pa

Conversion of pressure in Pa to mmHg

P = ρgh

Where,

P = Pressure

g = Acceleration due to gravity = 9.80665 m/s2

ρ = Density of mercury = 13595 kg/m3

`h=(P)/(\rho * g)\\=(398675)/(13595* 9.80665) =2.990329\ mHg`

`1 m = 10^(3)\ mmHg`

`2.990329\ m = 2.990329 * 10^3 = 2990.32\ mHg`