Chapter 13, Problem 100A

To determine

Pressure on the hull of a submarine at a depth of $65\text{m}$ .

Answer to Problem 100A

Pressure on a hull of a submarine is $7.4\times {10}^5\text{Pa}$ .

Explanation of Solution

Given:

Atmospheric pressure, $P_{atm}\text{= 1}\text{.01}\times {\text{10}}^5\text{Pa}$

Density of water, ${\rho }_{water}\text{= 1}\text{.00}\times {\text{10}}^3{\text{kg/m}}^3$

Acceleration due to gravity, $g\text{= 9}\text{.8}\text{N/kg}$

Height, $h\text{ = 65}\text{m}$

Formula used:

Pressure in liquid is

  $P=P_{atm}+\rho gh$

Where,

  $h$ is depth

  $\rho$ is density

  $g$ is gravitational field strength

  $P_{atm}$ is atmospheric pressure.

Calculation:

Apply the formula of pressure in Liquid, $P=P_{atm}\text{+}{\rho }_{water}gh$.

  $P\text{ = }\left(\text{1}\text{.01}\times {\text{10}}^5\text{Pa}\right)+\left(\text{1}\text{.00}\times {\text{10}}^3{\text{kg/m}}^3\right)\left(\text{9}\text{.8}\text{N/kg}\right)\left(\text{65}\text{m}\right)$

  $\text{= 7}\text{.4}\times {\text{10}}^5\text{Pa}$

  $\begin{array}{l}\\ \end{array}$

Conclusion:

Pressure on a hull of a submarine at a depth of 65m will be $7.4\times {10}^5\text{Pa}$ .