I’m studying aerodynamics. I understand Bernoulli’s principle very well, I just can't wrap my head around why pressure decreases as velocity increases. Like the garden hose example: if you cover the hose with your finger, water flows out of the hose faster (and somehow pressure decreases) but when the finger blocks the hole, wouldn't that add extra pressure on the fluid?
[Physics] Why does fluid pressure decrease as fluid velocity increases according to Bernoulli’s principle
aerodynamicsbernoulli-equationfluid dynamicspressurevelocity
Best Answer
This is a classic misunderstanding of Bernoulli's equation. What Bernoulli's equation actually says is that the velocity will increase in the direction of decreasing pressure: $P_2-P_1=-\frac12\rho(v_2^2-v_1^2)$. This makes sense: if the pressure is higher on the left than on the right, then the fluid will speed up to the right. This is just like if I pushed on a block with $5\,\rm N$ of force and you pushing on the block in the opposite direction with $10\,\rm N$ of force: the block would accelerate away from you and towards me, thus speeding up towards where the smaller force is being applied.
Yes, it would add extra pressure. Let's assume the hose is completely horizontal so that Bernoulli's equation for comparing the fluid inside the hose ($1$) and just outside the restriction ($2$) is (expressing pressures as gauge pressures)
$$P_1+\frac12\rho v_1^2=\frac12\rho v_2^2$$
And our constant flow rate $$A_1v_1=A_2v_2$$
Which gives us for the pressure $P_1$ and the velocity $v_2$: $$v_2=\frac{A_1}{A_2}v_1$$ $$P_1=\frac{(A_1^2-A_2^2)\rho v_1^2}{2A_2^2}$$
For a constant $\rho$, $v_1$, and $A_1$, both $P_1$ and $v_2$ increase with decreasing $A_2$ (i.e. the smaller the restriction the larger the pressure before the blockage and the larger the velocity right after the blockage). The larger pressure before the blockage as compared to after the blockage results in an acceleration of the fluid through the blockage.