How to get the units of momentum flux?

[AppeltjeBosheuvel]

Good evening,

Does anybody know how to get the units of momentum flux?
Momentum = kg m s−1
Flux = m−2 s−1

Somehow, I should end up with kg m-1 s-1
(kg m s−1) m−2 s−1 = kg m−1 s−1

However I end up with kg m-2 s-2

Is there anybody that knows what I'm doing wrong? :)

The units of momentum flux depend on the context and the specific physical quantity being described. In fluid dynamics, momentum flux is often associated with the flow of a fluid, and its units can be derived from the units of mass, velocity, and area. The standard unit of momentum flux in the International System of Units (SI) is the Newton per square meter (N/m²).

Here's how the units for momentum flux are derived:

• Momentum (p) has units of kilogram meters per second (kg·m/s).
• Area (A) has units of square meters (m²).

Therefore, the units of momentum flux (Φ) are:

Φ = p/A = (kg·m/s) / (m²) = kg/(m·s)

So, the SI unit for momentum flux is the kilogram per meter per second (kg/(m·s)). In fluid dynamics, this is commonly used to describe quantities like pressure, shear stress, or viscous forces.

Keep in mind that in different contexts, momentum flux may have different units. It's always important to consider the specific physical situation to determine the appropriate units for momentum flux.

 

[Orodruin]

Neither of those options is correct. Momentum flux is the transfer of momentum per area per time and should therefore has the dimensions $[p]/\mathsf{L^2 T} = \mathsf{(M L/T)/L^2 T}$ as you have identified. However, you made an arithmetic error. The correct arithmetics would give you the dimensions $\mathsf{M/LT^2}$. A unit for quantities of this physical dimension is kg/s^2m.

 

[AppeltjeBosheuvel]

Thanks!

So momentum flux = kg s-2 m-1 ?

On wiki it also says this:

1. Momentum flux, the rate of transfer of momentum across a unit area (N·s · m−2·s−1).

N = kg m s−2
N s = kg m s-1
N s flux = kg m s-1 m-2 s-1
Momentum flux = kg m-1 s-2
Same as you say.

However in my meteorology book it really says (kg m s−1) m−2 s−1 = kg m−1 s−1

So would this be a mistake in the book?

 

[Orodruin]

So would this be a mistake in the book?

Clearly.