An electromagnetic flowmeter is used to measure blood flow...

An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing $\mathrm{Na}^{+}$ ions flows due south through an artery with a diameter of $0.40 \mathrm{~cm}$. The artery is in a downward magnetic field of $0.25 \mathrm{~T}$ and develops a Hall voltage of $0.35 \mathrm{mV}$ across its diameter. (a) What is the blood speed (in $\mathrm{m} / \mathrm{s}$ )? (b) What is the flow rate (in $\mathrm{m}^{3} / \mathrm{s}$ )? (c) The leads of a voltmeter are attached to diametrically opposed points on the artery to measure the Hall voltage. Which of the two leads is at the higher potential?

An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing $\mathrm{Na}^{+}$ ions flows due south through an artery with a diameter of $0.40 \mathrm{~cm}$. The artery is in a downward magnetic field of $0.25 \mathrm{~T}$ and develops a Hall voltage of $0.35 \mathrm{mV}$ across its diameter. (a) What is the blood speed (in $\mathrm{m} / \mathrm{s}$ )? (b) What is the flow rate (in $\mathrm{m}^{3} / \mathrm{s}$ )?
(c) The leads of a voltmeter are attached to diametrically opposed points on the artery to measure the Hall voltage. Which of the two leads is at the higher potential?

Key Concepts

Lorentz Force

The Lorentz force is the force experienced by charged particles when they move within a magnetic field. In the context of electromagnetic flow measurement, the Lorentz force acts on the ions within the blood, displacing them in a direction perpendicular to both the flow and the magnetic field. This displacement generates the Hall voltage, which is crucial for calculating the speed of the blood flow.

Cross-sectional Area and Flow Rate

The cross-sectional area of a conduit, such as an artery, plays a critical role in determining the volumetric flow rate of a fluid. The flow rate is calculated as the product of the fluid speed and the cross-sectional area. Understanding this relationship is essential when converting the measured fluid velocity into an overall flow rate, thereby quantifying the amount of fluid passing through the system per unit time.

Electromagnetic Flowmeter

An electromagnetic flowmeter is a device used to measure the flow rate of electrically conductive fluids, such as blood, by exploiting the principle that a voltage is induced when a conductor moves through a magnetic field. This method is non-invasive and is particularly useful in medical settings, as it does not require physical intrusion into the fluid, thereby preserving the integrity of the flow and reducing the risk of contamination.

Hall Effect

The Hall effect is a phenomenon in physics where electrons moving through a conductor or semiconductor are deflected by a magnetic field, creating a measurable voltage perpendicular to both the direction of current flow and the magnetic field. This voltage, known as the Hall voltage, is used in electromagnetic flowmeters to determine the speed of the fluid, as it is directly proportional to the fluid’s velocity in the presence of the magnetic field.

Transcript

Please give Ace some feedback