Calculate the gauge pressure on an object at a depth of 20 m below the surface of a container filled with water.

Answer

To calculate the gauge pressure on an object at a depth of 20 m below the surface of a container filled with water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Gauge Pressure**:
Gauge pressure is the pressure relative to atmospheric pressure. It is the pressure exerted by the fluid at a certain depth without considering the atmospheric pressure acting on the surface.

2. **Identify the Formula**:
The formula for calculating the gauge pressure (P_g) at a depth (h) in a fluid is given by:
\[ P_g = \rho \cdot g \cdot h \]
where:
- \( \rho \) = density of the fluid (for water, it is approximately \( 1000 \, \text{kg/m}^3 \)),
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) = depth in meters.

3. **Substitute the Values**:
Given:
- \( \rho = 1000 \, \text{kg/m}^3 \) (density of water),
- \( g = 9.81 \, \text{m/s}^2 \),
- \( h = 20 \, \text{m} \).

Plugging these values into the formula:
\[ P_g = 1000 \, \text{kg/m}^3 \cdot 9.81 \, \text{m/s}^2 \cdot 20 \, \text{m} \]

4. **Calculate the Gauge Pressure**:
\[ P_g = 1000 \cdot 9.81 \cdot 20 = 196200 \, \text{Pa} \]
or in terms of Newton per square meter:
\[ P_g = 196200 \, \text{N/m}^2 \]

5. **Convert to Appropriate Units**:
Since gauge pressure is often expressed in kilopascals (kPa), we can convert it:
\[ P_g = \frac{196200 \, \text{N/m}^2}{1000} = 196.2 \, \text{kPa} \]

### Final Answer:
The gauge pressure at a depth of 20 m below the surface of the water is approximately **196.2 kPa**.