If the water pressure gauge shows the pressure at ground floor to be `270 k" ""Pa",` how high would water rise in the pipes of a building?

Answer

To solve the problem, we need to determine how high water would rise in the pipes of a building when the pressure gauge shows a pressure of 270 kPa. We will use the hydrostatic pressure formula, which relates the pressure at a certain depth in a fluid to the height of the fluid column above that point.

### Step-by-Step Solution:

1. **Understand the Given Pressure:**
The pressure given by the water gauge is \( P = 270 \, \text{kPa} \).
Convert this pressure into pascals:
\[ P = 270 \times 10^3 \, \text{Pa} = 270000 \, \text{Pa} \]

2. **Use the Hydrostatic Pressure Formula:**
The hydrostatic pressure formula is given by:
\[ P = \rho g h \]
where:
- \( P \) is the pressure (in pascals),
- \( \rho \) is the density of the fluid (for water, \( \rho \approx 1000 \, \text{kg/m}^3 \)),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height of the water column (in meters).

3. **Rearrange the Formula to Solve for Height \( h \):**
Rearranging the formula to find \( h \):
\[ h = \frac{P}{\rho g} \]

4. **Substitute the Known Values:**
Substitute \( P = 270000 \, \text{Pa} \), \( \rho = 1000 \, \text{kg/m}^3 \), and \( g = 9.81 \, \text{m/s}^2 \) into the equation:
\[ h = \frac{270000}{1000 \times 9.81} \]

5. **Calculate the Height \( h \):**
\[ h = \frac{270000}{9810} \approx 27.5 \, \text{m} \]

6. **Conclusion:**
Therefore, the height to which water would rise in the pipes of the building is approximately \( 27.5 \, \text{m} \).