A fountain sends water to a height of 116 m. What is the difference between the pressure of the water just before it is released upward and the atmospheric pressure? (The density of water is 1000 kg/m2.)
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rho g h = 1000 * 9.81 * 116 = 1.1*10^6 Pascals
To find the difference between the pressure of the water just before it is released upward and the atmospheric pressure, we can use the concept of pressure difference due to the height of the column of water.
The pressure at a certain depth in a fluid is given by 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 column of fluid.
In this case, we are interested in finding the pressure just before the water is released upward, which is at the bottom of the fountain. We know the height of the column of water is 116 m.
First, we need to calculate the pressure just before the water is released upward:
P_water = ρ * g * h
P_water = 1000 kg/m^2 * 9.8 m/s^2 * 116 m
P_water = 113,680 Pa
Next, we need to find the atmospheric pressure. The atmospheric pressure at sea level is approximately 101,325 Pa.
The difference in pressure is then given by:
Pressure difference = P_water - P_atm
Pressure difference = 113,680 Pa - 101,325 Pa
Pressure difference = 12,355 Pa
Therefore, the difference between the pressure of the water just before it is released upward and the atmospheric pressure is 12,355 Pa.