Respuesta :
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)
The pressure at the depth of the Marianas trench is [tex]\boxed{1.10\times{{10}^8}\,{\text{Pa}}}[/tex] .
Further Explanation:
Given:
The depth of the Marianas Trench is [tex]10.92\,{\text{km}}[/tex] .
The density of the sea water is [tex]1027\,{{{\text{kg}}}\mathord{\left/{\vphantom{{{\text{kg}}}{{{\text{m}}^{\text{3}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{m}}^{\text{3}}}}}[/tex] .
Concept:
The pressure due to a liquid varies due to the variation in the depth [tex]d[/tex] of the point from the surface. The variation of the pressure is given by:
[tex]P=\rho gh[/tex]
Here, [tex]P[/tex] is the pressure at the depth, [tex]\rho[/tex] is the density of the sea water, [tex]g[/tex] is the acceleration due to gravity and [tex]h[/tex] 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:
[tex]\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}[/tex]
Thus, the pressure at the depth of the Marianas trench is [tex]\boxed{1.10\times{{10}^8}\,{\text{Pa}}}[/tex] .
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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.
