Hydrostatics

A) Calculate the hydrostatic pressure at the bottom of the Mariana Trench.
The density of seawater is 1,030 kg/m³. What depth do you need to look up in an atlas or on the Internet?
B) Calculate the pressure force acting on a submarine with a surface area of 2,000 dm² at the bottom of this trench.
C) Calculate the pressure force acting on a hatch of a submarine, which has an area of 2,500 cm².

Final Answer:

p =  111.0867 MPa
F₁ =  2221733484 MN
F₂ =  27.7717 MN

Step-by-step explanation:

$$\begin{gathered} \rho =1030{\text{kg/m}}^3 \\ h=10994\text{m} \\ g=9.81{\text{m/s}}^2 \\ {p}_1=\rho \cdot g\cdot h=1030\cdot 9.81\cdot 10994=111086674.2\text{Pa} \\ p=p_1/10^6=111086674.2/10^6=111.0867\text{MPa} \end{gathered}$$

$$\begin{gathered} S_1=2000{\text{dm}}^2\to {\text{m}}^2=2000:100{\text{m}}^2=20{\text{m}}^2 \\ {F}_1=p_1\cdot S_1=111086674.2\cdot 20=2221733484\text{MN} \end{gathered}$$

$$\begin{gathered} S_2=2500{\text{cm}}^2\to {\text{m}}^2=2500:10000{\text{m}}^2=0.25{\text{m}}^2 \\ {F}_2=p\cdot S_2=111.0867\cdot 0.25=27.7717\text{MN} \end{gathered}$$

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