Normal atmospheric pressure is 1 atm, which is equivalent to 101.3 kPa. A mercury barometer measures atmospheric pressure by the height of the mercury column. Normally, this height is about 760 mm at sea level. When a storm approaches, the height of the mercury column drops by 20 mm, indicating a decrease in atmospheric pressure.
To find the new atmospheric pressure, we first need to understand the relationship between the height of the mercury column and the pressure. The pressure exerted by a column of mercury is given by the formula:
P = ρgh
where:
– P is the pressure,
– ρ is the density of mercury (approximately 13,600 kg/m³),
– g is the acceleration due to gravity (9.81 m/s²),
– h is the height of the mercury column.
First, convert the drop in height from mm to meters:
20 mm = 0.020 m
Now, calculate the pressure drop:
ΔP = ρgΔh
ΔP = (13,600 kg/m³) * (9.81 m/s²) * (0.020 m)
ΔP ≈ 2668.32 Pa
Subtract this pressure drop from the normal atmospheric pressure to find the new pressure:
New Pressure = 101,300 Pa – 2,668.32 Pa
New Pressure ≈ 98,631.68 Pa
Therefore, the new atmospheric pressure is approximately 98,632 Pa.