Question

A submarine is designed to withstand an absolute pressure of 100 atm. How deep can it go below the water surface? (Consider the density of water = 1000 kg m⁻³, 1 atm = 1 $\times$ 10⁵ Pa and g = 10 m/s²)

• A. 990 m
• B. 9000 m
• C. 99 m
• D. 9900 m

Hint:

Always remember that "absolute pressure" includes the 1 atm from the air above. If you forget to subtract it, you would incorrectly calculate 1000 m.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Absolute pressure at a certain depth in a fluid is the sum of the atmospheric pressure at the surface and the hydrostatic pressure exerted by the fluid column.

Step 2: Key Formula or Approach:
\[ P_{abs} = P_{atm} + \rho gh \]

Step 3: Detailed Explanation:
Given: $P_{abs} = 100$ atm, $P_{atm} = 1$ atm, $\rho = 1000$ kg/m³, $g = 10$ m/s². 1. Find the pressure exerted by the water only ($P_{gauge}$): \[ P_{gauge} = P_{abs} - P_{atm} = 100 - 1 = 99 \text{ atm} \] 2. Convert this pressure to Pascals: \[ P_{gauge} = 99 \times 10^5 \text{ Pa} \] 3. Use the hydrostatic pressure formula to find depth ($h$): \[ 99 \times 10^5 = 1000 \times 10 \times h \] \[ 9,900,000 = 10,000 \times h \] \[ h = \frac{9,900,000}{10,000} = 990 \text{ m} \]

Step 4: Final Answer:
The submarine can go to a depth of 990 m.