Question

The greatest ocean depths on the Earth are found in the Marianas Trench near the Philippines. Calculate the pressure due to the ocean at the bottom of this trench, given its depth is$11.0km$and assuming the density of seawater is constant all the way down.

Short answer

The pressure at $11km$into the sea is obtained as: $1.105\times {10}^{8}pa$.

Step-by-step solution

Conceptual Introduction

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

Given Data

The density of water is$\rho =1.025\times {10}^{3}kg/m^3$.

The depth at which pressure is to be calculated is$h=11km$.

If we convert it into the international standard unit $11km\times \left[\frac{1000m}{1km}\right]=11,000m$.

Calculating the pressure exerted at bottom

If we know the formula for pressure

$$\begin{gathered} \rho =\rho gh \\ =1.025\times {10}^3\times 9.8\times 11000 \\ =110495000Pa \\ =1.105\times {10}^{8}Pa \end{gathered}$$

Therefore, the pressure at eleven km into the sea is:$1.105\times {10}^{8}Pa$ .