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

In summary, the units of ϱ in the formula P = Patm + ϱgh should be in kg/m3, representing mass per volume.
  • #1
jumbogala
423
4

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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  • #2
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
 
  • #3
kPa has the same unit as Pa, which can be written as N/m2
 

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

What is density?

Density is a measure of how much matter is contained in a certain volume. It is often expressed in units of mass per unit volume, such as grams per cubic centimeter.

What are the SI units of density?

The SI unit of density is kilograms per cubic meter (kg/m3). Other commonly used units include grams per cubic centimeter (g/cm3) and grams per milliliter (g/mL).

How is density calculated?

Density is calculated by dividing the mass of an object by its volume. The formula for density is D=m/V, where D is density, m is mass, and V is volume. This formula is commonly used in physics and chemistry.

What is the difference between density and specific gravity?

Density and specific gravity are both measures of how compact or dense a substance is. However, density is an absolute measure, while specific gravity is a relative measure that compares the density of a substance to the density of water at a specific temperature. Specific gravity has no units, while density is expressed in units of mass per unit volume.

Why is it important to use the correct units when measuring density?

Using the correct units when measuring density is important because it ensures that the measurement is accurate and can be easily compared to other measurements. Using the wrong units can lead to confusion and incorrect calculations.

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