The water pressure on Mustafa as he dives is increasing at a rate of 0.9920.9920, point, 992 atmospheres (\text{atm})(atm)left parenthesis, a, t, m, right parenthesis per meter (\text{m})(m)left parenthesis, m, right parenthesis . What is the rate of increase in water pressure in \dfrac{\text{atm}}{\text{km}} ​km ​ ​atm ​​ start fraction, a, t, m, divided by, k, m, end fraction?

Accepted Solution

This problem is a simple dimensional analysis. We are simply tasked to express the rate 0.992 atm/m to atm/km.

Dimensional analysis, in simpler terms, is just the process of expressing an answer in another unit by multiplying conversion factors.

For this problem, we'll need to perform the following:

[tex] \frac{0.992 atm}{m}= \frac{1000m}{1km} = \frac{992atm}{km} [/tex]

Notice that we used the conversion factor 1000 meters = 1 kilometer to convert the units from atm/m to atm/km. Thus, we arrive at the final answer 992 atm/km.