Water towers store water above the level of consumers for times of
heavy use, eliminating the need for high-speed pumps. How high above
a user must the water level be to create a gauge pressure of
3.00×105 N/m2 ?
If you had a 1 m^2 pipe, what height would give a weight on the bottom of 3E5N?
weight water= mass*g= density*1m^2*height*9.8Nt/kg
= 1041 *9.8*height N
height= 3E5/(1041*9.8)= 29.4m
Now, to check: you know atomospheric pressure is about 10 m water height, so 300kpa/100kpa= 3 times atm pressure, so height is about 3*10 m
To determine the height above a user that the water level must be to create a gauge pressure of 3.00x10^5 N/m^2, we need to use the concept of pressure and elevation in a fluid.
The pressure at any point in a fluid is given by the formula:
P = ρgh
Where:
P is the pressure,
ρ (rho) is the density of the fluid,
g is the acceleration due to gravity,
h is the height above the point where the pressure is measured.
In this case, we want to find the height above a user, so we rearrange the formula:
h = P / (ρg)
Given that the gauge pressure P is 3.00x10^5 N/m^2, the density of water ρ is approximately 1000 kg/m^3, and the acceleration due to gravity g is approximately 9.81 m/s^2.
Substituting these values into the formula, we get:
h = (3.00x10^5 N/m^2) / (1000 kg/m^3 * 9.81 m/s^2)
Simplifying the equation, we find:
h = 30.57 meters
Therefore, the water level must be approximately 30.57 meters above a user to create a gauge pressure of 3.00x10^5 N/m^2.
To determine the height above a user that the water level must be to create a gauge pressure of 3.00x105 N/m2, we can use the formula for pressure:
P = ρgh
Where:
P = pressure (gauge pressure)
ρ = density of the fluid (water in this case)
g = acceleration due to gravity
h = height of the water column
Rearranging the formula to solve for h, we have:
h = P / (ρg)
Given that the gauge pressure is 3.00x105 N/m2 and the density of water is approximately 1000 kg/m3, and the acceleration due to gravity is approximately 9.8 m/s2, we can substitute these values into the equation:
h = 3.00x105 N/m2 / (1000 kg/m3 × 9.8 m/s2)
Simplifying the equation, we get:
h ≈ 3.06 meters
Therefore, the water level must be approximately 3.06 meters above a user to create a gauge pressure of 3.00x105 N/m2.