I have just been introduced to the Bernoulli Equation for fluid flow. However, I am unable to understand why the pressure and velocity are inversely proportional.
Because, as the fluid goes through a smaller cross-sectional area, the flow velocity increases, but due to the Bernoulli equation this increase in velocity means that there is a decrease in pressure. However, if say the fluid is not an ideal fluid, when it goes through a smaller cross section, it compresses, and hence is more "focused" therefore, it should surely mean that the pressure is increased. Furthermore, using the fundamental pressure equation:
P = F/A, a smaller cross-section will mean that there is more pressure.
I have seen all of the mathematical proof (the derivation of the Bernoulli equation), observed it in practice (using a U-tube manometer) and read some analogies to GPE to KE, but I still don't underdstand, physically how this can happen.
If someone has a good explanation, I would love to hear it, thanks.