Artery blockage. A medical technician is trying to determine...

Artery blockage. A medical technician is trying to determine what percentage of a patient's artery is blocked by plaque. To do this, she measures the blood pressure just before the region of blockage and finds that it is $1.20 \times 10^{4}$ Pa, while in the region of blockage it is $1.15 \times 10^{4}$ Pa. Furthermore, she knows that blood flowing through the normal artery just before the point of blockage is traveling at 30.0 $\mathrm{cm} / \mathrm{s}$ , and the specific gravity of this patient's blood is $1.06 .$ What percentage of the cross-sectional area of the patient's artery is blocked by the plaque?

Artery blockage. A medical technician is trying to determine what percentage of a patient's artery is blocked by plaque. To do this, she measures the blood pressure just before the
region of blockage and finds that it is $1.20 \times 10^{4}$ Pa, while in the region of blockage it is $1.15 \times 10^{4}$ Pa. Furthermore, she knows that blood flowing through the normal artery just before the point of blockage is traveling at 30.0 $\mathrm{cm} / \mathrm{s}$ , and the specific gravity of this patient's blood is $1.06 .$ What percentage of the cross-sectional area of the patient's artery is blocked by the plaque?

Key Concepts

Bernoulli's Principle

Bernoulli's Principle states that for an incompressible, non-viscous fluid, the sum of its pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline. This concept is crucial for relating the changes in pressure to the changes in the velocity of a fluid as it flows through regions of different cross-sectional areas.

Continuity Equation

The Continuity Equation is based on the conservation of mass for an incompressible fluid. It establishes that the product of the cross-sectional area and the fluid velocity is constant along a streamline. This principle is essential for understanding how variations in the area through which a fluid flows affect its velocity.

Specific Gravity and Density

Specific Gravity is the ratio of the density of a given fluid to the density of a reference substance, typically water. By knowing the specific gravity, one can calculate the actual density of the fluid, which is necessary when applying fluid dynamic principles, such as Bernoulli's equation, to determine effects like pressure differences.

Pressure-Flow Relationship in Fluids

The relationship between pressure and flow in fluids is governed by energy conservation principles. A change in fluid velocity, as caused by a narrowing of the flow channel, typically results in a corresponding change in pressure. Analyzing these pressure changes allows one to infer alterations in the cross-sectional area and understand the dynamics of the flow.

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