Fluid pressure problem and units confusion

[yoshtov]

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$^{3}$, 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$^{3}$ kg/m$^{3}$

The Attempt at a Solution

Doing what they did:

P = 101 kPa + 10$^{3}$*9.81 N/kg*10 m = 98,201 kPa = 972 atm.

Hmm... Trying it with atm:

P = 1 atm + 10$^{3}$*9.81 N/kg*10 m = 98,101 atm.

Trying it with Pa:

P = 101,325 Pa + 10$^{3}$*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?

 

[SammyS]

1 Pa = 1 N/m.

1kPa = 10³ N/m²

10³*9.81 N/kg*10 m = 9.81×10⁴ Pa = 98.1 kPa