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Nov 18, 2023

To solve this problem, we need to use the concept of hydrostatic pressure.

a) The gauge pressure at the bottom of the glass can be calculated using the formula:

P = ρgh

where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.

Given that the height of the water column is 30 cm, we can convert it to meters by dividing by 100:

h = 30 cm / 100 = 0.3 m

The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s².

Plugging in these values into the formula, we get:

P = (1000 kg/m³)(9.8 m/s²)(0.3 m) = 2940 Pa

Therefore, the gauge pressure at the bottom of the glass is 2940 Pa.

b) The absolute pressure at the bottom of the glass is the sum of the gauge pressure and the atmospheric pressure. The atmospheric pressure is typically around 101325 Pa.

Therefore, the absolute pressure at the bottom of the glass is:

P_absolute = P_gauge + P_atmospheric = 2940 Pa + 101325 Pa = 104265 Pa

Therefore, the absolute pressure at the bottom of the glass is 104265 Pa.

a) The gauge pressure at the bottom of the glass can be calculated using the formula:

P = ρgh

where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.

Given that the height of the water column is 30 cm, we can convert it to meters by dividing by 100:

h = 30 cm / 100 = 0.3 m

The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s².

Plugging in these values into the formula, we get:

P = (1000 kg/m³)(9.8 m/s²)(0.3 m) = 2940 Pa

Therefore, the gauge pressure at the bottom of the glass is 2940 Pa.

b) The absolute pressure at the bottom of the glass is the sum of the gauge pressure and the atmospheric pressure. The atmospheric pressure is typically around 101325 Pa.

Therefore, the absolute pressure at the bottom of the glass is:

P_absolute = P_gauge + P_atmospheric = 2940 Pa + 101325 Pa = 104265 Pa

Therefore, the absolute pressure at the bottom of the glass is 104265 Pa.