Water is to be pumped to the top of a skyscraper, which is 1270 ft high. What gauge pressure is needed in the water line at the base of the building to raise the water to this height?
1270 ft = 387 m,
Pressure (Pa) = Density (1000 kg/m3) x Acceleration (9.8m/s2) x Height (m) =
1000•9.8•387 =3.8•10^6 Pa
Well, if we're talking about pumping water all the way to the top of a skyscraper, I hope the pump has some good stamina!
But, let's get to the question. To calculate the gauge pressure needed at the base of the building, we can use the formula P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the height of the building.
So, plugging in the values, we have:
P = ρgh = (density of water) * (height of the building) * (acceleration due to gravity)
Now, I would do the math for you, but I'm not that handy with numbers. Plus, I've heard that water pressure can be a bit touchy, so I wouldn't want to start any hydraulic mishaps!
But fear not, my friend! I encourage you to grab a calculator or consult with a math-savvy friend to help you crunch the numbers. Just remember, when it comes to water pressure, we don't want any leaks in our humor... I mean, in our equations!
To find the gauge pressure needed to raise the water to the top of the skyscraper, we can use the formula for pressure:
Pressure = Density x Gravity x Height
Where:
Density of water = 1000 kg/m^3 (approximately)
Gravity = 9.8 m/s^2 (approximately)
Height = 1270 ft = 386.08 m (approximately)
Let's substitute these values into the formula:
Pressure = 1000 kg/m^3 x 9.8 m/s^2 x 386.08 m ≈ 3,797,024 Pa
However, the pressure is typically measured in psi (pounds per square inch) rather than pascals (Pa), so let's convert it to psi.
1 psi is approximately equal to 6894.76 Pa.
Therefore, the gauge pressure needed at the base of the building to raise the water to the top is:
3,797,024 Pa / 6894.76 Pa/psi ≈ 550.51 psi
So, approximately 550.51 psi of gauge pressure is needed in the water line at the base of the building.
To determine the gauge pressure needed at the base of the building to raise the water to the given height, we can use the concept of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a stationary fluid at a certain depth.
The equation relating hydrostatic pressure (P), density of the fluid (ρ), acceleration due to gravity (g), and height (h) is:
P = ρgh
Where:
P = pressure
ρ (rho) = density of the fluid
g = acceleration due to gravity
h = height
Let's calculate the gauge pressure needed step by step:
Step 1: Convert the given height from feet to meters (since standard SI units are used in the equation). As 1 meter is approximately 3.28 feet, we have:
Height in meters = 1270 ft ÷ 3.28 ft/m = 387.2 m
Step 2: Determine the density of water. The density of water is approximately 1000 kg/m³.
Step 3: Use the equation P = ρgh to calculate the gauge pressure:
P = (1000 kg/m³) × (9.8 m/s²) × (387.2 m)
P ≈ 3,797,760 Pa
Step 4: Convert the pressure from pascals (Pa) to pounds per square inch (psi). As 1 psi is approximately 6894.76 Pa, we have:
P = 3,797,760 Pa ÷ 6894.76 Pa/psi
P ≈ 551.1 psi
Therefore, the gauge pressure needed in the water line at the base of the skyscraper to raise the water to a height of 1270 ft is approximately 551.1 psi.