# Bernoulli Equation - Units Question

1. Apr 2, 2012

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:

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

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

2. Apr 2, 2012

### tiny-tim

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 )

3. Apr 2, 2012

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.

4. Apr 2, 2012

### tiny-tim

nooo, you need more sleep! :zzz:
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