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Stomach contents empty with an initial flow rate of 0.67 cm3/sec. Patients who undergo gastric bypass surgery will increase this rate by a factor of 16. Assuming that the flow of stomach contents approximates Poiseuille’s Law, what change to their gastrointestinal connection would explain this, provided no other changes occur that affect stomach content flow? A.The new connection is two times longer.B.The new connection is four times longer.C.The new connection radius is two times larger.D.The new connection radius is four times larger.

Question

Stomach contents empty with an initial flow rate of 0.67 cm3/sec. Patients who undergo gastric bypass surgery will increase this rate by a factor of 16. Assuming that the flow of stomach contents approximates Poiseuille’s Law, what change to their gastrointestinal connection would explain this, provided no other changes occur that affect stomach content flow? A.The new connection is two times longer.B.The new connection is four times longer.C.The new connection radius is two times larger.D.The new connection radius is four times larger.

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Solution

Poiseuille’s Law states that the flow rate (Q) through a tube is directly proportional to the fourth power of the radius (r) and inversely proportional to the length (L) of the tube. The equation is Q = πr^4ΔP/8ηL, where ΔP is the pressure difference and η is the viscosity.

Given that the flow rate increases by a factor of 16 and no other changes occur that affect stomach content flow, the only variable that could explain this is the radius of the gastrointestinal connection.

If the radius were to double (option C), the flow rate would increase by a factor of 2^4 = 16, which matches the given increase. Therefore, the new connection radius is two times larger.

Options A, B, and D can be ruled out. Doubling the length of the connection (option A) would halve the flow rate, not increase it. Quadrupling the length (option B) would reduce the flow rate to a quarter, not increase it. Quadrupling the radius (option D) would increase the flow rate by a factor of 4^4 = 256, which is much larger than the given increase.

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