Respuesta :
Since the surface of the sea is already at 1 atm therefore the pressure due to hydraulics is 4 atm.
We know that hydraulic pressure is:
P = ρ g h
where ρ is density, g is gravity and h is height
P = 1000 kg/m^3 * 9.81 m/s^2 * h = 4 atm * 101325 Pa / atm
h = 41.34 m = 135.5 feet
The depth at which the scuba diver experiences the pressure of [tex]5\,{\text{atm}}[/tex] is [tex]\boxed{135.2\,{\text{feet}}}[/tex].
Further Explanation:
Given:
The pressure experienced by the diver is [tex]5\,{\text{atm}}[/tex].
The pressure on the surface of the sea is [tex]1\,{\text{atm}}[/tex].
The density of the water is [tex]1\,{{\text{g}} \mathord{\left/{\vphantom {{\text{g}} {{\text{ml}}}}}\right.\kern-\nulldelimiterspace} {{\text{ml}}}}[/tex] or [tex]1000\,{{{\text{kg}}} \mathord{\left/{\vphantom {{{\text{kg}}} {{{\text{m}}^{\text{3}}}}}} \right.\kern-\nulldelimiterspace} {{{\text{m}}^{\text{3}}}}}[/tex].
Concept:
The pressure experienced by the scuba diver after diving to a certain depth is due to the pressure exerted by the amount of water present above the diver.
The pressure experienced by the scuba diver is the sum of the atmospheric pressure and the hydraulic pressure of the amount of water present above him. Thus, the pressure due to water is expressed as:
[tex]{P_{water}} = {P_{total}} - {P_{atm}}[/tex]
The atmospheric pressure is considered as [tex]1\,{\text{atm}}[/tex].
Substitute the values in above expression.
[tex]\begin{aligned}{P_{water}}&=5\,{\text{atm}}-1\,{\text{atm}}\\&= 4\,{\text{atm}} \times \left( {1.01 \times {{10}^5}} \right)\,{\text{Pa}}\\&= 4.{\text{04}} \times {\text{1}}{{\text{0}}^5}\,{\text{Pa}}\\\end{aligned}[/tex]
Now, the pressure due to a certain height of water present above the scuba diver is given by:
[tex]{P_{water}}=\rho gh[/tex]
Here, [tex]\rho[/tex] is the density of the water, [tex]g[/tex] is the acceleration due to gravity and [tex]h[/tex] is the height of water above the diver.
Substitute the values in above expression.
[tex]\begin{aligned}4.04\times{10^5}&=1000\times9.8\timesh\\h&=\frac{{4.04\times{{10}^5}}}{{1000 \times 9.8}}\\&= 41.22\,{\text{m}}\times{\text{3}}{\text{.28}}\,{\text{ft}}\\{\text{135}}&={\text{.2}}\,{\text{ft}}\\\end{aligned}[/tex]
Thus, the depth at which the scuba diver experiences the pressure of [tex]5\,{\text{atm}}[/tex] is [tex]\boxed{135.2\,{\text{feet}}}[/tex].
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Pressure
Keywords: Scuba diver, experiencing a pressure, 5 atm, depth in feet, atmospheric pressure, hydraulic pressure, height of water, 135.2 feet.
