Question

In an electromagnetic blood flow meter, the induced voltage is directly proportional to the

• A. blood flow rate
• B. square root of blood flow rate
• C. square of blood flow rate
• D. logarithm of the blood flow rate

Hint:

Faraday's Law of Induction yields a highly linear relationship ($E \propto Q$).
This linearity is why electromagnetic flow meters are highly accurate and widely used in biomedical applications.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question asks about the relationship between the induced voltage in an electromagnetic blood flow meter and the physiological parameter being measured.

Step 2: Key Formula or Approach:
The electromagnetic blood flow meter operates on Faraday's Law of Electromagnetic Induction.
When a conducting fluid (blood containing ions) flows through a magnetic field, a voltage is induced across the vessel. The induced voltage $E$ is given by:
\[ E = B \cdot d \cdot v \] where:
$B$ is the magnetic field strength,
$d$ is the blood vessel diameter, and
$v$ is the average velocity of the blood flow.

Step 3: Detailed Explanation:

• The volumetric blood flow rate ($Q$) through a vessel of cross-sectional area $A$ is related to the average velocity $v$ by the equation:
\[ Q = A \cdot v \implies v = \frac{Q}{A} \]
• Substituting this into the induced voltage equation:
\[ E = B \cdot d \cdot \frac{Q}{A} \]
• For a circular blood vessel of diameter $d$, the area is $A = \frac{\pi d^2}{4}$. Substituting this gives:
\[ E = B \cdot d \cdot \frac{Q}{\pi d^2 / 4} = \frac{4 B Q}{\pi d} \]
• Since the magnetic field $B$ and vessel diameter $d$ remain constant during measurement, the induced voltage $E$ is directly proportional to the volumetric blood flow rate ($Q$):
\[ E \propto Q \]

Step 4: Final Answer:
The induced voltage is directly proportional to the blood flow rate.