Final answer:
To find the height h₃ when the absolute pressure at point A is 114,200 Pa, use the hydrostatic pressure equation, rearrange for h₃, and substitute the values of density (13.6 g/cm³) and gravity (9.81 m/s²). After unit conversion, h₃ is found to be 847 mm.
Step-by-step explanation:
The question is asking for the height h₃ when the absolute pressure at point A is given as 114,200 Pa. However, the provided information does not include the numerical values from part (c), which are needed to calculate the height h₃. Thus, it is not possible to determine the value of h₃ without that additional information. Please provide the numerical values from part (c) in order to solve for the height h₃.
To explain the calculation for the height h₃ given that the absolute pressure at point A is 114,200 Pa, we can use the hydrostatic pressure equation. Given that the density (ρ) of mercury is 13.6 g/cm³ and the acceleration due to gravity (g) is 9.81 m/s², we can find height h₃ by rearranging the hydrostatic pressure formula:
p = hρg
First, convert the density of mercury from g/cm³ to kg/m³ (since 1 g/cm³ = 1000 kg/m³) to use consistent SI units:
13.6 g/cm³ = 13600 kg/m³
Now solve for h₃ by rearranging the formula:
h₃ = p / (ρg)
Substitute the known values into the equation:
h₃ = 114,200 Pa / (13600 kg/m³ × 9.81 m/s²)
This yields:
h₃ = 0.847 m or 847 mm
Therefore, the height h₃ is 847 mm.