Answer :
Answer:
1) The pressure difference is 4.207 kilopascals.
2) 2.5 pounds per square inch equals 5.093 inches of mercury and 5.768 feet of water.
Explanation:
1) We can calculate the gas pressure difference from the U-tube manometer by using the following hydrostatic formula:
[tex]\Delta P = \frac{S\cdot \rho_{w}\cdot g \cdot \Delta h}{1000}[/tex] (Eq. 1)
Where:
[tex]S[/tex] - Relative density, dimensionless.
[tex]\rho_{w}[/tex] - Density of water, measured in kilograms per cubic meter.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]\Delta h[/tex] - Height difference in the U-tube manometer, measured in meters.
[tex]\Delta P[/tex] - Gas pressure difference, measured in kilopascals.
If we know that [tex]S = 1.5[/tex], [tex]\rho_{w} = 1000\,\frac{kg}{m^{3}}[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]\Delta h = 0.286\,m[/tex], then the pressure difference is:
[tex]\Delta P = \frac{1.5\cdot \left(1000\,\frac{kg}{m^{3}} \right)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (0.286\,m)}{1000}[/tex]
[tex]\Delta P = 4.207\,kPa[/tex]
The pressure difference is 4.207 kilopascals.
2) From Physics we remember that a pound per square unit equals 2.036 inches of mercury and 2.307 feet of water and we must multiply the given pressure by corresponding conversion unit: ([tex]p = 2.5\,psi[/tex])
[tex]p = 2.5\,psi\times 2.037\,\frac{in\,Hg}{psi}[/tex]
[tex]p = 5.093\,in\,Hg[/tex]
[tex]p = 2.5\,psi\times 2.307\,\frac{ft\,H_{2}O}{psi}[/tex]
[tex]p = 5.768\,ft\,H_{2}O[/tex]
2.5 pounds per square inch equals 5.093 inches of mercury and 5.768 feet of water.