Convert the pressure 225 kPa into units of millimeters of mercury and meters of water. Specific gravity of Hg of
=13.6, and use g=10 m/s^2
= 1000 kg/m³ h = P/
g Use the grid method to compute the pressure as a height of liquid. mmmHg and mH
O
The Correct Answer and Explanation is:
Correct Answer:
Given:
- Pressure P=225 kPa=225,000 PaP = 225 \, \text{kPa} = 225,000 \, \text{Pa}P=225kPa=225,000Pa
- Acceleration due to gravity g=10 m/s2g = 10 \, \text{m/s}^2g=10m/s2
- Density of water ρwater=1000 kg/m3\rho_{\text{water}} = 1000 \, \text{kg/m}^3ρwater=1000kg/m3
- Specific gravity of mercury SG=13.6SG = 13.6SG=13.6, hence ρHg=13.6×1000=13,600 kg/m3\rho_{\text{Hg}} = 13.6 \times 1000 = 13,600 \, \text{kg/m}^3ρHg=13.6×1000=13,600kg/m3
1. Convert to meters of water (mH₂O):
The height hhh of a liquid column is found using the formula:h=Pρgh = \frac{P}{\rho g}h=ρgPhwater=225,0001000×10=22.5 m of waterh_{\text{water}} = \frac{225,000}{1000 \times 10} = 22.5 \, \text{m of water}hwater=1000×10225,000=22.5m of water
2. Convert to millimeters of mercury (mmHg):
hHg=225,00013,600×10=225,000136,000=1.65441 m of mercuryh_{\text{Hg}} = \frac{225,000}{13,600 \times 10} = \frac{225,000}{136,000} = 1.65441 \, \text{m of mercury}hHg=13,600×10225,000=136,000225,000=1.65441m of mercury1.65441 m=1654.41 mm1.65441 \, \text{m} = 1654.41 \, \text{mm}1.65441m=1654.41mm
Final Answers:
- 225 kPa = 1654.41 mmHg
- 225 kPa = 22.5 mH₂O
Explanation:
Pressure represents the force exerted per unit area. When expressing pressure as the height of a liquid column, the relationship P=ρghP = \rho g hP=ρgh provides a method for converting a pressure value into the height of an equivalent column of liquid.
To determine the height of a water column corresponding to a pressure of 225 kilopascals, the density of water (1000 kg/m³) and gravitational acceleration (10 m/s²) are used. By rearranging the formula to isolate height hhh, dividing the pressure by the product of density and gravity provides the water column height. This results in a height of 22.5 meters of water.
For mercury, the specific gravity indicates that mercury is 13.6 times denser than water. Therefore, its density becomes 13,600 kg/m³. Substituting into the same formula with mercury’s density yields a much shorter column, due to the higher density. The height comes out to be approximately 1.654 meters or 1654.41 millimeters.
This method of pressure conversion is valuable in fields like fluid mechanics and meteorology, where pressure readings are often presented in terms of fluid column heights. The higher the density of the liquid, the shorter the column needed to balance a given pressure. Mercury, being dense, requires a shorter column compared to water for the same pressure. Thus, 225 kPa can be equally represented as 1654.41 mmHg or 22.5 mH₂O.
