Pressure vs speed for liquids ?

Main Question or Discussion Point

pressure vs speed for liquids ? :(

Think of a pipe positioned horizontally.

Some fluid is flowing from left to right.(e.g. water)

Right side of the pipe is well narrower than left side.

Is the speed of a fluid particle at the right greater than the speed of a particle at the left?

(Perfect world no energy loss)
OR

perhaps I can NOT make such a comparison without considering any value constant.

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I am really confused please help , basically I am looking for an example which prooves inverse proportion of speed and pressure of LIQUIDS. Can you give me an example like mine? Thank you for your help...

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Astronuc
Staff Emeritus
Let's assume an incompressible fluid - the density does not change - and apply conservation of mass.

$\rho_1 * V_1 * A_1 = \rho_2 * V_2 * A_2$

for incompressible flow $\rho_1 = \rho_2 = \rho$

which then leaves $V_1 * A_1 = V_2 * A_2$

So what does the say about the relationship between fluid velocity (speed) and area?

ok that's well ...

that means fluid flows faster in the narrow section. That is completely different from my thought.

Is it the same if we use Bernoulli's equation to see that?

I could't see where is the pressure difference

Considering the fluid is incompressible, helps by making density constant. Is it the pressure difference, that causes the fluid to flow faster at the place where the pipe narrows???

You should take it the other way round(you should obviously apply Bernoulli's equation), that static head drop occurs due to increase in velocity head.