Problem 21.25: Measuring blood flow. Part A Blood contains positive and negative

Question

Problem 21.25: Measuring blood flow. Part A Blood contains positive and negative ions, so it is a conductor. A blood vessel, therefore, can be viewed as an electrical wire. We can even picture the flowing blood as a series of parallel conducting slabs whose thickness is the diameter d of the vessel moving with speed u (See Figure 1).) If the blood vessel is placed in a magnetic field B perpendicular to the vessel, as in the figure, determine the expression for the motional potential difference induced across it. Express your answer in terms of v, B, and d. Submit My Answers Give Up Part B If you expect that the blood will be flowing at 15.2 cm/s for a vessel 4.95 mm in diameter, what strength of magnetic field will you need to produce a potential difference of 1.00 mV? Express your answer in teslas to three significant figures. Figure 1 ¢of! Submit My Answers Give Up Part C Determine the volume rate of flow (R) of the blood. (Note: Although the method developed here is useful in measuring the rate of blood flow in a vessel, it is limited to use in surgery because measurement of the potential must be made directly across the vessel.) Express your answer in terms of E, d, B, and the appropriate constants.

Explanation / Answer

a)

motional emf is given as

E = B v d

b)

v = 15.2 cm/s = 0.152 m/s

d = 4.95 x 10-3 m

E = 1 x 10-3 T

using the equation

E = B v d

0.001 = B (0.152) (4.95 x 10-3)

B = 1.33 T

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