A vacuum gauge reads 10” Hg when the atmospheric pressure is 30” Hg. Assuming the
density of mercury to be 13595 kgm/m3
, determine the absolute pressure in kPaa.
Answer
Well, this is quite the pressure situation we have here! Let's do some calculations, shall we?
First, let's convert the measurements to a more common unit for pressure, shall we? We'll convert the atmospheric pressure from inches of mercury to kilopascals (kPa).
We know that 1 inch (in) of mercury (Hg) is approximately equal to 3.38639236 kilopascals (kPa). So, 30 inches of mercury would be around 101.592769078 kPa (I promise I didn't make that number up).
Now, let's tackle the vacuum gauge reading. It's displaying 10 inches of mercury. This means that the pressure exerted by the vacuum is 20 inches less than atmospheric pressure. So, we subtract 20 inches from our previous atmospheric pressure measurement.
101.592769078 kPa - 20 inches * 3.38639236 kPa/in = 65.78513878 kPa (approximately).
Now, we have the pressure in kilopascals caused by the vacuum. But hold on, we're not done yet! We need to convert this pressure to pascals because the density of mercury is in kilograms per cubic meter (kg/m³).
One kilopascal (kPa) is equal to 1000 pascals (Pa). So, multiplying our pressure by 1000, we get:
65.78513878 kPa * 1000 = 65785.13878 Pa (approximately).
Phew! Now we're ready to calculate the absolute pressure.
The formula for absolute pressure is P = P₀ + ρgh, where P is the absolute pressure, P₀ is the atmospheric pressure, ρ is the density of the fluid (mercury in this case), g is the acceleration due to gravity, and h is the height difference.
Substituting the values we know:
P = 65785.13878 Pa + 13595 kg/m³ * 9.8 m/s² * 0 (since the height difference is 0 in this case, as it is a vacuum).
Simplifying a bit:
P = 65785.13878 Pa.
So, the absolute pressure in kilopascals is approximately 65.78513878 kPa.
I hope this answer doesn't suck too much!
To determine the absolute pressure in kPaa, we need to convert the pressure values given in inches of mercury (Hg) to the desired unit of kilopascals (kPa).
1. Convert the atmospheric pressure from inches of mercury to kilopascals:
- Given: Atmospheric pressure = 30” Hg
- Conversion factor: 1” Hg = 3.38638867 kPa (approximately)
- Calculation: 30” Hg * 3.38638867 kPa/1” Hg ≈ 101.5916601 kPa
- Therefore, the atmospheric pressure is approximately 101.59 kPa.
2. Convert the vacuum pressure from inches of mercury to kilopascals:
- Given: Vacuum pressure = 10” Hg
- Calculation: 10” Hg * 3.38638867 kPa/1” Hg ≈ 33.8638867 kPa
- Therefore, the vacuum pressure is approximately 33.86 kPa.
3. Calculate the absolute pressure by adding the atmospheric pressure and the vacuum pressure:
- Calculation: Atmospheric pressure + Vacuum pressure ≈ 101.59 kPa + 33.86 kPa ≈ 135.45 kPa
- Therefore, the absolute pressure is approximately 135.45 kPa.
Note: "kPaa" refers to kilopascals absolute, where the pressure is measured relative to absolute zero pressure.
To determine the absolute pressure in kPaa (kilopascal absolute), we need to understand the relationship between vacuum pressure and atmospheric pressure and convert the units accordingly.
Vacuum pressure is measured relative to atmospheric pressure, so to obtain the absolute pressure, we need to add the vacuum pressure to the atmospheric pressure.
In this case, the vacuum gauge reads 10" Hg (inches of mercury) when the atmospheric pressure is 30" Hg.
First, we need to convert the vacuum pressure from inches of mercury to pascal.
To convert inches of mercury to pascal, we can use the following conversion factors:
1 inch of mercury = 3386.39 pascal
So, 10" Hg = 10 * 3386.39 = 33863.9 pascal
Now, we need to convert the atmospheric pressure from inches of mercury to pascal as well.
30" Hg = 30 * 3386.39 = 101590.7 pascal
Finally, we can calculate the absolute pressure by adding the vacuum pressure to the atmospheric pressure.
Absolute pressure = atmospheric pressure + vacuum pressure
Absolute pressure = 101590.7 + 33863.9 = 135454.6 pascal
To convert pascal to kPaa, divide the value by 1000.
Absolute pressure in kPaa = 135454.6 / 1000 = 135.4546 kPaa
Therefore, the absolute pressure is approximately 135.4546 kPaa.