I feel like every time I do a problem like this I get a different answer... I thought that if you decrease the area, then pressure INCREASES like in vasoconstriction. Is Kaplan's answer wrong for thinking Bernoulli's equation applies since the heart isn't an ideal system?
I had the same problem with these kinds of questions too. It helps to take this idea of a narrowing artery to the extreme. What if you had an artery that suddenly narrowed dramatically to like 0.1mm? You wouldn't have much pressure on the artery walls on the other side. The blood would be traveling very fast, but with hardly any pressure. It's like taking a hose and sticking your thumb over it. The water travels much faster, which according to Bernoulli, must be due to a decrease in pressure.
You could also use math to prove to yourself that this idea of decreased pressure with a decreased opening has to be true. Looking at the diagram, decreasing r would mean an increase in R(resistance). Since volume flowrate is a constant (what goes in must come out), we can assume that the change in pressure must be larger, because R became larger. Hope that helps!
I like to use the continuity equation to first figure out how a smaller area will change velocity.
a1v1 = a2v2. If a2 < a1, then v2 should be greater than v1. So velocity is increasing through a smaller cross section.
Then Bernoulli's equation relates this change to pressure.
P1 + density1 * g * h1 + 1/2 * density1 * v1^2 = P2 + density2 * g * h2 + 1/2 * density2 * v2^2. I bolded the important parts of the equation as we're assuming h1 = h2. Since v2 > v1, P2 will be less than P1.