# Bernoulli's Principle question

I have in my notes that as speed of a fluid increases, density decreases.
This doesn't make sense to me. When a fluid passes through a narrower area, doesn't that mean that its density is increasing because it is now packed more tightly together? If this is the case, shouldn't the rule be that as speed increases, density increases (in accordance with the concept that a fluid passing through a narrower area speeds up to maintain flow rate)?

I also have in my notes that as pressure increases, density increases.
As I stated in the previous paragraph, it seems to me that as speed increases, density should also increase. However, Bernoulli's Principle states that as a fluid's speed increases, pressure decreases. So shouldn't the rule be that as pressure increases, density decreases? (If someone helps me understand the rule from the first paragraph, I'll likely be able to figure this rule out on my own).

Thank you

Bernoulli's principle is so interesting because of this counter-intuitiveness!

The way I like to think of it is that energy density in a fluid is constant. In a formula:

pressure + .5*density*velocity^2 + mass*g*density*vertical displacement = constant

It should be clear from this that increasing velocity decreases pressure or decreases density (usually pressure).

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"increasing velocity increases pressure"

I thought the whole idea of Bernoulli's principle was that increasing velocity decreases pressure...???

I mistyped, I've edited it.

stewartcs
I have in my notes that as speed of a fluid increases, density decreases.
This doesn't make sense to me. When a fluid passes through a narrower area, doesn't that mean that its density is increasing because it is now packed more tightly together? If this is the case, shouldn't the rule be that as speed increases, density increases (in accordance with the concept that a fluid passing through a narrower area speeds up to maintain flow rate)?

I also have in my notes that as pressure increases, density increases.
As I stated in the previous paragraph, it seems to me that as speed increases, density should also increase. However, Bernoulli's Principle states that as a fluid's speed increases, pressure decreases. So shouldn't the rule be that as pressure increases, density decreases? (If someone helps me understand the rule from the first paragraph, I'll likely be able to figure this rule out on my own).

Thank you

For incompressible flow the density will be constant. This is the typical assumption (one of them any way) with the Bernoulli Principle.

For compressible flow, the density will vary depending on the pressure. As the pressure increases the density increases and vice versa.

CS

Hmm. Okay.
Another question, then.
Is the following statement true?:
the narrower the pipe, the higher the density