Poiseuille’s hagen lawis
**Core Concept**
Poiseuille's law describes the laminar flow of a Newtonian fluid through a cylindrical pipe, which is an essential concept in fluid dynamics and hemodynamics. This law is crucial in understanding blood flow through arteries and veins, as well as the flow of other fluids through narrow tubes.
**Why the Correct Answer is Right**
Poiseuille's law states that the flow rate (F) of a fluid is directly proportional to the pressure difference (ΔP) between the two ends of the pipe, the fourth power of the radius (r) of the pipe, and inversely proportional to the length (l) and viscosity (η) of the fluid. The correct formula is F = (PA - PB) × 3.14 × r^4 / 8ηl, where PA and PB are the pressures at the two ends of the pipe. This formula demonstrates the relationship between the pressure difference and the radius of the pipe, which is a critical factor in determining the flow rate.
**Why Each Wrong Option is Incorrect**
**Option B:** This option incorrectly adds the pressures at the two ends of the pipe, which would result in a flow rate that is not dependent on the pressure difference. This is not consistent with the principles of fluid dynamics.
**Option C:** This option incorrectly uses the ratio of the pressures at the two ends of the pipe, which would result in a flow rate that is not dependent on the pressure difference. This is not consistent with the principles of fluid dynamics.
**Option D:** This option incorrectly multiplies the pressures at the two ends of the pipe, which would result in a flow rate that is not dependent on the pressure difference. This is not consistent with the principles of fluid dynamics.
**Clinical Pearl / High-Yield Fact**
Remember that Poiseuille's law is essential in understanding blood flow through arteries and veins, which is critical in the diagnosis and management of vascular diseases. The law can be used to calculate the flow rate of blood through a vessel, which can be useful in determining the severity of stenosis or other vascular abnormalities.
**✓ Correct Answer: A. F = (PA–PB) × 3.14 × r^4/8ηl**