# Step-by-Step Solution: Pressure at 5 m Depth in Water ## 1. **Formula for Pressure Due to a Fluid Column** The pressure at a depth \( h \) below the surface of a liquid is given by: \[ P = P_ + \rho g h \] Where: - \( P \): Total pressure at depth \( h \) - \( P_ \): Atmospheric pressure on the surface (often ignored for gauge pressure) - \( \rho \): Density of the liquid (\( 100 \) kg/m³ for water) - \( g \): Acceleration due to gravity (\( 9.81 \) m/s²) - \( h \): Depth below the surface (\( 5 \) m) If only the **gauge pressure** (pressure above atmospheric) is required: \[ P_{\text{gauge}} = \rho g h \] --- ## 2. **Substitute the Values** Given: - \( \rho = 100 \) kg/m³ - \( g = 9.81 \) m/s² - \( h = 5 \) m Plug these values into the formula: \[ P_{\text{gauge}} = 100 \times 9.81 \times 5 \] --- ## 3. **Calculate the Pressure** \[ P_{\text{gauge}} = 100 \times 9.81 \times 5 = 100 \times 49.05 = 49,050 \text{ Pa} \] --- ## 4. **Final Answer** **The gauge pressure at 5 m below the water surface is:** \[ \boxed{49,\!050\ \text{Pa}} \] Or, in kilopascals: \[ \boxed{49.05\ \text{kPa}} \]