How high (in meters) would the water rise in the pipes of a building if the water pressure gauge shows the pressure to be 252 kPa at ground level?
I assume that is gauge pressure, not absolute.
weight of a column of water h high with diameter of 1m^2:
weight=h*1*1E3kg/m^3*9.8N/kg
pressure from that (weight /area)
pressure=h*1E3*9.8 N/m^2=9.8h kPa
252kPa=9.8 kPa * h
h=252/9.8 meters
At whatever level the water rises to, only atmospheric pressure shall be actung on the meniscus. Hence, the height it reaches will be h=100/9.8
To determine how high the water would rise in the pipes of a building, we need to consider the relationship between water pressure and height in a closed vertical pipe system.
The equation we can use is given by:
P = ρgh
Where:
P = Pressure (in Pascals or N/m²)
ρ = Density of water (approximately 1000 kg/m³)
g = Acceleration due to gravity (approximately 9.8 m/s²)
h = Height (in meters)
In this case, we are given the pressure as 252 kPa (kiloPascals), but we need to convert it to Pascals to use it in the equation.
1 kPa = 1000 Pa
So, 252 kPa = 252,000 Pa
Now, let's rearrange the equation to find the height, h:
h = P / (ρg)
Substituting the given values:
h = 252,000 Pa / (1000 kg/m³ * 9.8 m/s²)
Calculating this:
h ≈ 25.71 meters
Therefore, the water would rise approximately 25.71 meters in the pipes of the building if the water pressure gauge shows a pressure of 252 kPa at ground level.