At the surface of a freshwater lake, the pressure is 105 kPa.
What is the pressure increase in going 42.3 m below the surface? The density of fresh water at 4°C is 1.00 × 103 kg/m3. (kPa)

To find the pressure increase at a depth of 42.3 m below the surface of a freshwater lake, we can use the hydrostatic pressure formula:

\[
\Delta P = \rho \cdot g \cdot h
\]

Where:
- \( \Delta P \) = pressure increase (in Pascals)
- \( \rho \) = density of water ( \( 1.00 \times 10^3 \, \text{kg/m}^3 \) )
- \( g \) = acceleration due to gravity ( \( 9.81 \, \text{m/s}^2 \) )
- \( h \) = depth ( \( 42.3 \, \text{m} \) )

Now, let's plug in the values:

\[
\Delta P = (1.00 \times 10^3 \, \text{kg/m}^3) \cdot (9.81 \, \text{m/s}^2) \cdot (42.3 \, \text{m})
\]

\[
\Delta P = 415.263 \times 10^3 \, \text{Pa} = 415.263 \, \text{kPa}
\]

Thus, the pressure increase at a depth of 42.3 m is approximately **415.26 kPa**.

Would you like to dive deeper into the topic or have further questions?

Here are 5 related questions:
1. How does the pressure vary with different water densities?
2. What would be the pressure increase at a depth of 100 m?
3. How does pressure behave in saltwater compared to freshwater?
4. How does temperature affect the density and, therefore, pressure in water?
5. How is this pressure increase relevant for divers or submarines?

**Tip**: Always convert units to match the system you're working in, especially when dealing with pressure and force.

At the surface of a freshwater lake, the pressure is 105 kPa. What is the pressure increase in going 42.3 m below the surface? The density of fresh water at 4°C is 1.00 × 103 kg/m3. (kPa)

Learn how to calculate the pressure increase at a depth of 42.3 m below the surface of a freshwater lake. This problem involves concepts from hydrostatics, using the formula ΔP = ρ * g * h with the water density 1.00 × 103 kg/m³ and gravity 9.81 m/s². Suitable for Grades 11-12 physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation