Bernoulli Equation - Units Question

JJBladester

1. The problem statement, all variables and given/known data

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

2. Relevant equations

The Bernoulli equation for steady, incompressible flow is:

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

3. 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!
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

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

nooo, you need more sleep!