A closed-end tube is evacuated and placed with its open end beneath the surface of a reservoir of water. The water rises to a height of 9.5 m. If the density of water is 1000 kg/m^3, what is the pressure at the bottom of the column of water?
To find the pressure at the bottom of the column of water, you can use the concept of hydrostatic pressure.
Hydrostatic pressure is given by the equation: 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 column of fluid.
In this case, the fluid is water and its density is given as 1000 kg/m^3. The height of the column of water is 9.5 m.
Now, substitute the given values into the equation:
P = (1000 kg/m^3) * (9.8 m/s^2) * (9.5 m)
Calculate:
P ≈ 92,050 Pa
So, the pressure at the bottom of the column of water is approximately 92,050 Pascal (Pa).
To find the pressure at the bottom of the column of water, we will use the formula for pressure:
Pressure = Density × Gravitational Acceleration × Height
Given:
Density of water (ρ) = 1000 kg/m³
Height (h) = 9.5 m
Gravitational Acceleration (g) = 9.8 m/s²
Plugging in the values into the formula, we get:
Pressure = 1000 kg/m³ × 9.8 m/s² × 9.5 m
Calculating the above expression, we can find:
Pressure = 92,150 Pa
Therefore, the pressure at the bottom of the column of water is 92,150 Pa.