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Chapter 14: Q13P (page 407)

At a depth of 10.9 km, the Challenger Deep in the Marianas Trench of the Pacific Ocean is the deepest site in any ocean. Yet, in 1960, Donald Walsh and Jacques Piccard reached the Challenger Deep in the bathyscaph Trieste. Assuming that seawater has a uniform density of1024kg/m3, approximate the hydrostatic pressure (in atmospheres) that the Trieste had to withstand. (Even a slight defect in the Trieste structure would have been disastrous.)

Short Answer

Expert verified

Hydrostatic pressure in atmospheres is1.08脳103atm

Step by step solution

01

The given data

  • Density of seawater,p=1024kg/m3
  • Depth,h=10.9kmor10.9脳103m
02

Understanding the concept of hydrostatic pressure

To solve for pressure, we can use the formula for hydrostatic pressure difference, which depends on density and height. Hydrostatic pressure is that, which is exerted by a fluid at any point of time at equilibrium due to the force applied by gravity.

Formula:

Pressure applied on a fluid surface, p = pgh (i)

03

Calculation of hydrostatic pressure in atmospheres

Using equation (i) and the given values, the pressure can be written as:

p=1024kg/m3脳9.8m/s2脳10.9脳103mp=1.09脳108Pa(鈭�1atm=1.01脳105Pa)=1.09脳108脳1atm1.01脳105=1.08脳103atm

Hence, the value of hydrostatic pressure is1.08脳103atm

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