The water pressure in the mains of a city at a particular location is 269 kPa gage. Determine the fluid column height in "meter unit" corresponding to the given gage pressure. The density of water is taken to be ρ = 1000 kg/m3.
Question
The water pressure in the mains of a city at a particular location is 269 kPa gage. Determine the fluid column height in "meter unit" corresponding to the given gage pressure. The density of water is taken to be ρ = 1000 kg/m3.
Solution
To solve this problem, we need to use the formula for pressure in a fluid column, which is P = ρgh, where:
- P is the pressure,
- ρ is the fluid density,
- g is the acceleration due to gravity, and
- h is the height of the fluid column.
We are given P = 269 kPa, ρ = 1000 kg/m^3, and we know that g = 9.81 m/s^2. We want to find h.
First, we need to convert the pressure from kPa to Pa, because 1 kPa = 1000 Pa. So, P = 269,000 Pa.
Next, we rearrange the formula to solve for h:
h = P / (ρg)
Substituting the given values:
h = 269,000 Pa / (1000 kg/m^3 * 9.81 m/s^2)
This gives us h = 27.43 meters. So, the fluid column height corresponding to the given gage pressure is approximately 27.43 meters.
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