**ERIC Number:**EJ875462

**Record Type:**Journal

**Publication Date:**2004

**Pages:**5

**Abstractor:**As Provided

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0740-8404

Poiseuille's Law--Showing that "p" Is Inversely Proportional to R[superscript 4] Using the Shell Method

Drost, John P.; Georges, Rachel A.

AMATYC Review, v25 n2 p11-15 Spr 2004

Jean Poiseuille, a physician, developed a mercury filled U-tube to measure blood pressure in 1828. He discovered that pressure in veins is significantly lower than pressure in arteries. As a result, he studied liquid flow in small tubes. A few years later he established Poiseuille's Law, which states the resistance, "p," of the flow of blood as "p" = K(L/R[superscript 4]) where L and R are the length and radius of the vessel respectively. K is a positive constant determined by the viscosity of the blood. It is curious that the resistance is inversely proportional to the fourth power of the radius R. At first glance, most individuals may assume the resistance should be inversely proportional to the second power of the radius since the area of a circle is [pi]R[superscript 2]. In this article, mathematics, including finding volume using cylindrical shells, is developed to establish that the resistance is indeed inversely proportional to the fourth power of the radius.

Descriptors: Mathematics Instruction, Mathematical Concepts, College Mathematics, Community Colleges, Measurement Techniques

American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: amatyc@amatyc.org; Web site: http://www.amatyc.org

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Two Year Colleges

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A