Determine the minimum gauge pressure needed in the water pipe leading into a building if water is to come out of a faucet on the twelfth floor, 41m above that pipe.
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To determine the minimum gauge pressure needed in the water pipe, we can use the concept of pressure and height difference.
The gauge pressure is the pressure measured above atmospheric pressure. In this case, we need to calculate the minimum gauge pressure at the water pipe to ensure that the water reaches the twelfth floor, which is 41 meters above the pipe.
We can use the formula for pressure:
P = ρgh
Where:
P is the pressure (in Pascals)
ρ is the density of the fluid (in kilograms per cubic meter)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height difference (in meters)
In this case, we need to find the gauge pressure, so we will use the difference in height (41m) between the faucet on the twelfth floor and the water pipe.
1. Determine the density of water:
The density of water is approximately 1000 kg/m^3.
2. Calculate the gauge pressure:
Using the formula P = ρgh, substitute the known values:
P = (1000 kg/m^3) * (9.8 m/s^2) * (41 m)
P = 401,800 Pa
Therefore, the minimum gauge pressure needed in the water pipe leading into the building is 401,800 Pascal (Pa).