Bernoulli Equation - Units Question

[JJBladester]

Homework Statement

My book says that each term in the Bernoulli equation (when divided by ρ, has pressure units). I don't see how.

Homework Equations

The Bernoulli equation for steady, incompressible flow is:

[tex]\frac{P}{\rho}+\frac{V^{2}}{2}+gz=constant[/tex]

The Attempt at a Solution

Multiplying the Bernoulli equation by density (ρ), we get:

[tex]P+\rho\frac{V^{2}}{2}+\rho gz=constant[/tex]

ρ = kg/m³ units

V²=m⁶ units

ρV²=kg*m³ units

How does the middle term in the Bernoulli equation with the units listed above count as having pressure units?

Pressure = Force/Area = Newtons/m²= [itex]\frac{\frac{kg\cdot m}{s^2}}{m^2}=\frac{kg}{m\cdot s^2}[/itex]

 

[tiny-tim]

Hi JJBladester!

V²=m⁶ units

Nooo …

V is velocity! ​

(btw, Bernouilli's equation is essentially a conservation of energy equation, which is why you get a sort-of mv²/2 term )

 

[JJBladester]

Hi JJBladester!

Nooo …

V is velocity! ​

I need more coffee. Wow, I wish I could unpost that last post.

Thanks for the reply, though. It makes a lot of sense now.

 

[tiny-tim]

I need more coffee.

nooo, you need more sleep! :zzz:

 

[asteriatic]

=\frac{mass}{length\cdot time^2}

The middle term in the Bernoulli equation, ρV2/2, can be rewritten as:

\frac{kg}{m\cdot s^2} \cdot \frac{m^2}{s^2}=\frac{kg}{m\cdot s^2}

This shows that the units of ρV2/2 are indeed equivalent to pressure units. In fact, ρV2/2 is known as dynamic pressure, which is a type of pressure that is associated with the movement of a fluid. Therefore, the middle term in the Bernoulli equation does have pressure units.