What Are the Correct Units for Density in the Equation P = Patm + ϱgh?

[jumbogala]

Homework Statement

I'm dealing with densities of liquids.

When using the formula P = P_atm + ϱgh, where ϱ is the density of the liquid, what should the units of ϱ be?

Homework Equations

The Attempt at a Solution

I have P in kPa, so just looking at the units gives:
kPa = kPa + (?)(m/s²)(m) --> kPa = (?)(m²/s²)

Which would mean the units of ϱ are (kPa)(s² / m²).

Somehow that seems wrong... I thought ϱ was supposed to have units of mass per volume?

 

[ehild]

1 Pa = 1 N m^-2
1 kPa = 1000 Pa
1 atm = 101.325 kPa

1 N=1kg m s^-2

So 1 atm = 101325kg m^-1s^-2 in the basic Si units.

ehild

 

[rock.freak667]

kPa has the same unit as Pa, which can be written as N/m²