- #1
yoshtov
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Homework Statement
Exercise Find the pressure at a depth of 10 m below the
surface of a lake if the pressure at the surface is 1 atm.
(Answer: With P0 = 1atm = 101kPa, ρ=103kg/m[itex]^{3}[/itex], and g= 9.81 N/kg, we have P = P0 + ρgh = 1.97 atm. The pressure at a depth of 10 m is nearly twice that at the surface.)
Homework Equations
P = P0 + ρgh
1 atm = 101.325 kPa = 101325 Pa
ρ = 10[itex]^{3}[/itex] kg/m[itex]^{3}[/itex]
The Attempt at a Solution
Doing what they did:
P = 101 kPa + 10[itex]^{3}[/itex]*9.81 N/kg*10 m = 98,201 kPa = 972 atm.
Hmm... Trying it with atm:
P = 1 atm + 10[itex]^{3}[/itex]*9.81 N/kg*10 m = 98,101 atm.
Trying it with Pa:
P = 101,325 Pa + 10[itex]^{3}[/itex]*9.81 N/kg*10 m = 199,425 Pa = 1.97 atm.
So I was only able to get the answer they did when using Pa. I think they neglected to mention that pivotal part when solving the problem. I have questions two:
1). Why does the equation have a strong preference for Pa?
2). How would I have to restructure the equation to use kPa, atm, or mmHg?