ab open tube mercury manometer is used to measure the pressure in an oxygen tank. when the atmospheric pressure is 1040 mbar, what is the absolute pressure (in Pa) in the tank if the height of the mercury in the open tube is
a)28 cm higher
b)4.2cm lower, than the mercury in the tube connected to the tank.
Ptank - Po = (mercury density)*g*(delta H)
where delta H = (outside column height) - (column height on tank side)
thankyou!
To determine the absolute pressure in the tank, we need to consider the difference in heights between the mercury levels in the open tube and the tube connected to the tank. We will use the following conversion factors:
1 cm = 0.01 m
1 mbar = 100 Pa
Given:
Atmospheric pressure = 1040 mbar
a) If the height of the mercury in the open tube is 28 cm higher than the mercury in the tube connected to the tank.
In this case, the pressure difference between the two mercury levels is the same as the pressure due to the additional height of the mercury column.
Converting the height to meters:
28 cm × 0.01 m/cm = 0.28 m
The pressure due to the additional height is given by the hydrostatic pressure formula:
Pressure = ρgh,
where:
ρ = density of mercury (13,595 kg/m³)
g = acceleration due to gravity (9.8 m/s²)
h = height (0.28 m)
Calculating the pressure due to the additional height:
Pressure = 13,595 kg/m³ × 9.8 m/s² × 0.28 m = 3,817.34 Pa
To find the absolute pressure in the tank:
Absolute pressure = Atmospheric pressure + Pressure due to additional height
Absolute pressure = 1040 mbar × 100 Pa/mbar + 3,817.34 Pa
Absolute pressure = 104,000 Pa + 3,817.34 Pa
Absolute pressure = 107,817.34 Pa
Therefore, the absolute pressure in the tank when the height of the mercury in the open tube is 28 cm higher is 107,817.34 Pa.
b) If the height of the mercury in the open tube is 4.2 cm lower than the mercury in the tube connected to the tank.
In this case, the pressure difference between the two mercury levels is the same as the pressure due to the difference in height between them.
Converting the height difference to meters:
4.2 cm × 0.01 m/cm = 0.042 m
The pressure due to the difference in height is calculated in the same way as in part a:
Pressure = 13,595 kg/m³ × 9.8 m/s² × 0.042 m = 5,647.02 Pa
To find the absolute pressure in the tank:
Absolute pressure = Atmospheric pressure - Pressure due to difference in height
Absolute pressure = 104,000 Pa - 5,647.02 Pa
Absolute pressure = 98,352.98 Pa
Therefore, the absolute pressure in the tank when the height of the mercury in the open tube is 4.2 cm lower is 98,352.98 Pa.
To solve this problem, we need to understand how an open tube mercury manometer works. In an open tube manometer, the height difference between the two mercury columns indicates the pressure difference between the two ends of the manometer. The equation we can use to relate the pressure difference and the height difference is:
ΔP = ρgh
Where:
ΔP is the pressure difference in Pascals (Pa)
ρ is the density of mercury, which is 13,595 kg/m³
g is the acceleration due to gravity, approximately 9.8 m/s²
h is the height difference in meters (m)
We can now proceed to solve the problem:
a) When the height of the mercury in the open tube is 28 cm higher than the mercury in the tube connected to the tank:
First, we convert the height difference to meters:
h = 28 cm / 100 cm/m = 0.28 m
Next, we substitute the values into the equation:
ΔP = ρgh = 13,595 kg/m³ * 9.8 m/s² * 0.28 m = 3,628.84 Pa
Therefore, the absolute pressure in the tank is 3,628.84 Pa.
b) When the height of the mercury in the open tube is 4.2 cm lower than the mercury in the tube connected to the tank:
First, we convert the height difference to meters:
h = -4.2 cm / 100 cm/m = -0.042 m (negative because the height is lower)
Next, we substitute the values into the equation:
ΔP = ρgh = 13,595 kg/m³ * 9.8 m/s² * -0.042 m = -5,029.56 Pa
Since the height is lower than the reference point (tube connected to the tank), the pressure difference is negative. Therefore, the absolute pressure in the tank is decreased by 5,029.56 Pa.
Note: To calculate the absolute pressure in the tank, we need to add the calculated pressure difference to the atmospheric pressure.
I hope this explanation helps you understand how to solve the problem and apply the concepts of an open tube mercury manometer! Let me know if there's anything else I can assist you with.