Your town is installing a fountain in the main square. If the water is to rise 20 m above the fountain, how much pressure must the water have as it moves slowly toward the nozzle that sprays it up into the air? Assume atmospheric pressure equal to 100,000 Pa.
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To calculate the pressure of the water as it moves towards the nozzle, we need to use the concept of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a fluid at rest and depends on the height of the fluid column and the density of the fluid.
The formula for hydrostatic pressure is:
Pressure = Density × gravitational acceleration × height
In this case, the height is the 20 m above the fountain that the water needs to rise, and the density of water is approximately 1,000 kg/m³. The value of gravitational acceleration is approximately 9.8 m/s².
Let's plug in these values to calculate the pressure:
Pressure = 1,000 kg/m³ × 9.8 m/s² × 20 m
Calculating this, we get:
Pressure = 196,000 Pa
However, this is just the pressure due to the height of the water column. We also need to consider the atmospheric pressure, which is given as 100,000 Pa.
To find the total pressure, we add the pressure due to the water column to the atmospheric pressure:
Total pressure = Pressure due to water column + Atmospheric pressure
Total pressure = 196,000 Pa + 100,000 Pa
Calculating this, we get:
Total pressure = 296,000 Pa
Therefore, the water must have a pressure of 296,000 Pa as it moves towards the nozzle that sprays it up into the air.