A fountain sends water to a height of 149 m. What is the difference between the pressure of the water just before it is released upward and the atmospheric pressure?
To calculate the difference between the pressure of the water just before it is released upward and the atmospheric pressure, we can use the concept of hydrostatic pressure.
The hydrostatic pressure at a certain depth in a fluid is given by the equation:
P = ρgh
Where:
P is the pressure at the chosen depth,
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the height or depth from the surface.
In this case, the height or depth (h) is the height to which the water is being sent, which is 149 m.
The density (ρ) of water is approximately 1000 kg/m³, and the acceleration due to gravity (g) is 9.8 m/s².
Therefore, we can calculate the hydrostatic pressure just before the water is released upward:
P = (1000 kg/m³) * (9.8 m/s²) * (149 m) = 1,454,200 Pa
This is the pressure of the water just before it is released upward.
The atmospheric pressure at sea level is commonly considered to be 101,325 Pa (or 101.325 kPa).
So, to calculate the difference in pressure, we subtract the atmospheric pressure from the pressure of the water just before it is released upward:
Difference in pressure = Pressure of water just before release - Atmospheric pressure
Difference in pressure = 1,454,200 Pa - 101,325 Pa = 1,352,875 Pa
Therefore, the difference between the pressure of the water just before it is released upward and the atmospheric pressure is approximately 1,352,875 Pa (or 1352.875 kPa).