A water tower sits on top of a hill and supplies water to citizens below. The difference in pressure between the water tower and the Dailey's house is 1.1x10^5 Pa, while the difference in pressure between the tower and the Stearns' house is 3.2x10^5 Pa. a)which house sits at a higher elevation? b)what is the difference in elevation between the twoo houses?
The lower house gets the higher pressure.
difference in pressure between 2 houses = (3.2-1.1)*10^5 Pascals or Newtons/meter^2
difference in pressure = rho g * difference in height
a) Well, it's clear that Dailey's house has a lower elevation. The pressure difference at their house is less than at Stearns' house, so it must be sitting lower.
b) As for the difference in elevation, we can calculate it using the pressure difference. Let's perform a hilarious mathematical trick! By using the pressure difference and some equation wizardry, we can relate pressure to elevation.
So, the difference in pressure (3.2x10^5 - 1.1x10^5 Pa) is equal to the density of water (ρ) times the acceleration due to gravity (g) times the difference in elevation (h).
Now, let's substitute the values we know. Oh, and by the way, I'm using density (ρ) as an alias for "Clown Juice".
(3.2x10^5 - 1.1x10^5) = ρgh
Solving for h (the difference in elevation), we get h = (3.2x10^5 - 1.1x10^5) / (ρg).
Now, I apologize for the anticlimax, but the value of h will depend on the density of water (Clown Juice). So, without knowing that, we can't solve for the exact difference in elevation between the two houses. But hey, feel free to estimate it with your favorite density of water. Just remember, the answer will be in meters, not laughs!
To determine which house sits at a higher elevation and find the difference in elevation between the two houses, we can use the relationship between pressure and elevation in a fluid.
The pressure difference between two points in a fluid is directly proportional to the difference in elevation between those points. This can be described by the equation:
ΔP = ρgh
where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the difference in elevation.
Let's assume that the density of water is ρ = 1000 kg/m^3, and the acceleration due to gravity is g = 9.8 m/s^2.
a) To determine which house sits at a higher elevation, we compare the pressure differences given. From the information provided, the pressure difference between the water tower and the Dailey's house is 1.1x10^5 Pa, while the pressure difference between the water tower and the Stearns' house is 3.2x10^5 Pa. Since the pressure difference is greater for the Stearns' house, we can conclude that it sits at a higher elevation compared to the Dailey's house.
b) To find the difference in elevation between the two houses, we can use the equation ΔP = ρgh. Rearranging the equation to solve for h, we have:
h = ΔP / (ρg)
For the Dailey's house:
h_Dailey = (1.1x10^5 Pa) / (1000 kg/m^3 * 9.8 m/s^2)
h_Dailey = 11.22 meters
For the Stearns' house:
h_Stearns = (3.2x10^5 Pa) / (1000 kg/m^3 * 9.8 m/s^2)
h_Stearns = 32.65 meters
Therefore, the difference in elevation between the two houses is:
Δh = h_Stearns - h_Dailey
Δh = 32.65 m - 11.22 m
Δh ≈ 21.43 meters
So, the Stearns' house sits at a higher elevation, and the difference in elevation between the two houses is approximately 21.43 meters.
To determine the relative elevation between the two houses, we can use the concept of pressure difference and the equation for hydrostatic pressure.
a) To determine which house sits at a higher elevation, we need to compare the pressure differences. The pressure difference is directly related to the difference in elevation between the water tower and the houses.
We can use the equation for hydrostatic pressure:
P = ρgh
where P is the pressure, ρ is the density of the fluid (water, in this case), g is the acceleration due to gravity, and h is the height or elevation.
By comparing the pressure differences given, we can infer that the house with the larger pressure difference (3.2x10^5 Pa) is located at a higher elevation, as the pressure increases with depth.
b) To find the difference in elevation between the two houses, we can subtract the pressure differences at each house and relate it to the density of water and acceleration due to gravity.
Let's assume the density of water is ρw = 1000 kg/m^3 and the acceleration due to gravity is g = 9.8 m/s^2.
For Dailey's house:
P_Dailey = ρwgh_Dailey
For Stearns' house:
P_Stearns = ρwgh_Stearns
Given that P_Stearns - P_Dailey = 3.2x10^5 Pa - 1.1x10^5 Pa = 2.1x10^5 Pa, we can equate the two expressions for pressure:
ρwgh_Stearns - ρwgh_Dailey = 2.1x10^5 Pa
Since the density and acceleration due to gravity are the same, they cancel out:
h_Stearns - h_Dailey = 2.1x10^5 Pa / (ρw x g)
Substituting the values, we have:
h_Stearns - h_Dailey = (2.1x10^5 Pa) / (1000 kg/m^3 x 9.8 m/s^2)
Calculating the difference in elevation:
h_Stearns - h_Dailey = 2142.85 meters
Therefore, the difference in elevation between the two houses is approximately 2142.85 meters.