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:

$$\frac{P}{\rho}+\frac{V^{2}}{2}+gz=constant$$

The Attempt at a Solution

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

$$P+\rho\frac{V^{2}}{2}+\rho gz=constant$$

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

 

[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: