Variation of Pressure with Depth

[jer_hall99]

Homework Statement

By what factor is the total pressure greater at a depth of 850 m of sea water than at the surface where the pressure is one atmosphere? (water density = 1000 kg/m3, one atmosphere pressure = 1.01 x 105 Pascals (N/m2), g = 9.8 m/s2 )

Homework Equations

P=P(initial)+ρgh

The Attempt at a Solution

P=(1.01x10^5)+(1000kg/m^3*9.8m/s^2*850m)

 

[technician]

Your calculation gives you the pressure at the depth of 850m. The question is worded...'by what factor is the total pressure greater at a depth of 850m... I think this means you are expected to give your answer as a ratio??

 

[jer_hall99]

ok, well how would I do that? the possible answers to the question are a. 100, b. 83, c. 74, d. 19. That is where I am stuck.

 

[technician]

using P = hρg I got the pressure due to the water to be 8.33 x 10^6 Pa
Atmospheric pressure is 1.01 x 10^5 Pa
Get the ratio ?

 

[asteriatic]

= 8.585x10^8 Pascals (N/m^2)

The factor by which the total pressure is greater at a depth of 850 m compared to the surface is approximately 8.48x10^3. This means that the pressure at 850 m is about 8480 times greater than the pressure at the surface. This makes sense, as the pressure increases with depth due to the weight of the water above pushing down. At a depth of 850 m, there is a significant amount of water above that is adding to the pressure. This calculation also takes into account the density of water, as well as the acceleration due to gravity.