(a) Explanation Given information: Consider a blood vessel with radius 0.01 cm, length 3 cm, pressure difference 3000 dynes/cm 2 and viscosity η = 0.027 . Calculation: The law of Laminar flow states that for a given blood vessel with radius R , length l cm, pressure difference P and viscosity η , the blood at radius r away from the central axis of the vessel flows at a velocity v given by: v = P 4 η l ( R 2 − r 2 ) Realizing that R = 0.01 cm, l = 3 cm, P = 3000 dynes/cm 2 and η = 0.027 the velocity along the center-line r = 0 is v ( 0 ) = 3000 4 ( 3 ) ( 0.027 ) [ ( 0.01 ) 2 − 0 2 ] = 0.926 cm/s The velocity at radius r = 0.005 cm is v ( 0 (b) To determine To find: velocity gradient at r = 0, r = 0.005 and r = 0.01. (c) To determine To describe: Where is the velocity the greatest? Where is the velocity changing most?

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Question

Chapter 3.3, Problem 49E

(a)

To determine

To find:velocity of the blood along the centerline r = 0, at radius r = 0.005 cm and at the wall r = R = 0.01 cm.

(b)

To determine

To find:velocity gradient at r = 0, r = 0.005 and r = 0.01.

(c)

To determine

To describe:Where is the velocity the greatest? Where is the velocity changing most?

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Chapter 3.3, Problem 48E

Chapter 3.3, Problem 50E

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Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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velocity of the blood along the centerline r = 0, at radius r = 0.005 cm and at the wall r = R = 0.01 cm.

Solution Summary: The law of Laminar flow states that for a given blood vessel with radius R, length l cm, pressure difference P and viscosity, the blood at radius r away from the central axis of the vessel

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To find:velocity of the blood along the centerline r = 0, at radius r = 0.005 cm and at the wall r = R = 0.01 cm.

To find:velocity gradient at r = 0, r = 0.005 and r = 0.01.

To describe:Where is the velocity the greatest? Where is the velocity changing most?

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Chapter 3 Solutions