The liquid in the open tube manometer is mercury, y1=3cm and y2 = 7cm. Atmospheric pressure is 980mbrs. (A) what is the absolute pressure at the bottom of the U-shape tube? (B) what is the absolute pressure in the open tube at a depth of 4 cm below the free surface? (C) what is the absolute pressure of the gas in the tank? (D) what is the gauge pressure of the gas in pascal
To solve this problem, we will use the equation for pressure difference in a manometer, which is given by:
ΔP = ρgh
where:
ΔP is the pressure difference,
ρ is the density of the liquid in the manometer (mercury in this case),
g is the acceleration due to gravity, and
h is the difference in height of the liquid columns.
Given values:
y1 = 3 cm
y2 = 7 cm
Atmospheric pressure = 980 mbrs
(A) To find the absolute pressure at the bottom of the U-shape tube, we need to consider the pressure due to the liquid column above it and the atmospheric pressure. The pressure difference between the two sides of the manometer gives us the pressure difference between the bottom of the U-shape tube and atmospheric pressure.
ΔP = P_bottom - P_atmospheric
Using the equation for pressure difference, we can write:
ΔP = ρgh
Let's calculate the pressure difference, ΔP:
ΔP = ρg(y2 - y1)
ΔP = (density of mercury)(acceleration due to gravity)((7 cm) - (3 cm))
Note: Make sure to convert all the values into consistent units. Acceleration due to gravity (g) can be taken as 9.8 m/s² for this calculation.
(B) To find the absolute pressure in the open tube at a depth of 4 cm below the free surface, we need to consider the pressure due to the liquid column above it and the atmospheric pressure. Here, the pressure difference is the pressure at the open tube minus the atmospheric pressure.
ΔP = P_open tube - P_atmospheric
Using the equation for pressure difference:
ΔP = ρgh
Let's calculate the pressure difference, ΔP:
ΔP = ρg(h + y1)
ΔP = (density of mercury)(acceleration due to gravity)((4 cm) + (3 cm))
(C) To find the absolute pressure of the gas in the tank, we need to consider the pressure due to the liquid column in the manometer and the atmospheric pressure. The pressure difference is the pressure inside the tank plus the pressure at the open tube minus the atmospheric pressure.
Absolute pressure of the gas in the tank = P_gas in tank + P_open tube - P_atmospheric
(D) Finally, to calculate the gauge pressure, we subtract the atmospheric pressure from the absolute pressure:
Gauge pressure = Absolute pressure - P_atmospheric
Please note that you need to know the density of mercury, which is approximately 13,600 kg/m³, to calculate the pressure difference.