Question

The deepest point known in any of the earth's oceans is in the marianas trench, 10.92 km deep. assuming water to be incompressible, what is the pressure at this depth? (use density of seawater 1027 kg/m3).]\

Answer 1

The pressure at the depth of the Marianas trench is $\boxed{1.10\times{{10}^8}\,{\text{Pa}}}$ .

Further Explanation:

Given:

The depth of the Marianas Trench is $10.92\,{\text{km}}$ .

The density of the sea water is $1027\,{{{\text{kg}}}\mathord{\left/{\vphantom{{{\text{kg}}}{{{\text{m}}^{\text{3}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{m}}^{\text{3}}}}}$ .

Concept:

The pressure due to a liquid varies due to the variation in the depth $d$  of the point from the surface. The variation of the pressure is given by:

$P=\rho gh$

Here, $P$  is the pressure at the depth, $\rho$  is the density of the sea water, $g$  is the acceleration due to gravity and  $h$ is the depth from the surface.

Substitute the values of the density, acceleration die to gravity and the depth of the point from the surface in the above expression:

$\begin{aligned}P&=1027\times9.81\times\left({10.92\times{{10}^3}}\right)\,{\text{Pa}}\\&=1007.48\times10.92\times{10^3}\,{\text{Pa}}\\&=1.10\times{10^8}\,{\text{Pa}}\\\end{aligned}$

Thus, the pressure at the depth of the Marianas trench is $\boxed{1.10\times{{10}^8}\,{\text{Pa}}}$ .

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Answer Details:

Grade: Middle School

Subject: Physics

Chapter: Pressure

Keywords:

Deepest point, Marianas Trench, Earth’s oceans, 10.92 km, water is incompressible, density of sea water, depth, pressure, p=rho x g x h.

Answer 2

The solution for the problem is:

 

The pressure of a column of fluid = rho g h

 

Where: rho = density,

 

g = 9.81m/s/s, and

 

h = depth 

at 10.92km: 

P = 1027kg * 9.81m/s/s * 10920 m

 

= 1027 kg x 107125.2

 

= 1.10 x 10^8 Pa (the MKS unit of pressure)