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

AI Thread Summary
In the equation P = Patm + ϱgh, the correct units for density (ϱ) should indeed reflect mass per volume. Given that pressure (P) is in kPa, the derived units for ϱ from the equation suggest it should be in kg/m³, aligning with standard density units. The discussion clarifies that 1 kPa equals 1000 Pa, and since 1 Pa is equivalent to N/m², which can be expressed in SI units as kg/(m·s²), it confirms that ϱ must be in kg/m³. The confusion arises from manipulating the equation, but the fundamental understanding of density remains consistent with its definition. Thus, the units for density in this context should be kg/m³.
jumbogala
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Homework Statement


I'm dealing with densities of liquids.

When using the formula P = Patm + 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?
 
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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
 
kPa has the same unit as Pa, which can be written as N/m2
 

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