TBR CBT 2 - Question 20 (Flow rate)

[DeFused]

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As a fluid flows through a tube whose radius steadily decreases from 2.0 to 1.0 cm, what change can be expected if the indicated factor remains constant?

A. If flow rate is constant, then ∆P must increase
B. If flow rate is constant, then ∆P must decrease
C. If ∆P is constant, then R must increase
D. If ∆P is constant, then η must increase

I got this question right because they gave Poiseulle's law in the passage: (Change in Pressure) * (pi * R^4)/(8nL) - so if radius decreases and flow rate is constant then pressure must increase.

As I a reviewing this problem I was thinking about Bernoulli's principle where it states that an increase in velocity will decrease the pressure. If flow rate is constant in this example wouldn't velocity increase as well? (Q = VA) and an increase in velocity will result in a decrease in pressure?

**Edit: the passage is just describing blood flow

 

[sdm33]

Based on Bernoulli's principle B looks good, but if passages is saying something else then go with the passage.

 

[DeFused]

Is there a reason why Bernoulli's principle doesn't apply here though?

 

[sdm33]

I think it depends on the flow type like laminar flow and Poiseuille flow (viscosity) When a fluid travels through a tube, the leading end looks like a bullet traveling through air (basically, it's not inverted).
Berneoulli's Law describes the ideal case, conservation of energy in a fluid that flows without friction, a fluid with no viscosity, or internal friction.

Pouseuille's Law describes the dissipation of energy as a real fluid encounters the friction of the pipe.

Both laws have appeared on many MCATs, although with Pouseuille's Law, the passage is more likely to give you an orientation than in a passage dealing with Bernoulli's. With Bernoulli's Law, you are more likely to be expected to reason conceptually without being given the formula.

Bernoulli's is higher on the scale of required knowledge. Pouseuille's Law is the kind of thing that shows up a lot, but the exam would likely present the formula and a short discussion within the passage.