Jean-Louis-Marie Poiseuille was a French physician and physiologist who formulat

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Jean-Louis-Marie Poiseuille was a French physician and physiologist who formulated a mathematical expression for the flow rate for the laminar (non-turbulent) flow of fluids in circular tubes. Discovered independently by Gotthilf Hagen, a German hydraulic engineer, this relation is also known as the Hagan-Poiseuille equation. As you can imagine, this mathematical model is of great interest to physiologists who study blood flow, hydraulic engineers, and builders of oil pipelines. Picture a cylindrical tube that carries fluid. Obviously, to move the fluid through the tube, there must be pressure on the fluid at one end of the tube. The Hagen-Poiseuille Law states that the pressure needed to maintain a flow through the tube is proportional to the length of the tube, L, the flow rate Q (in volume per unit time), and inversely proportional to the fourth power of the radius of the tube, R. Write the Hagen-Poiseuille Law. Identify the factors that definitely cannot affect the value of the proportionality constant, and at least two factors that clearly would affect the value of the proportionality constant. What happens to the pressure if the length of the tube doubles? Explain. What happens to the pressure if the radius is cut in half? Explain. Is Q proportional to L or inversely proportional to L'l Is Q proportional or inversely proportional to R4? Explain. What happens to the flow rate if the radius is cut in half? Explain. Rearrange the equation so that Q is the output. Now, we will hold all variables constant except Q and R. Many people who have clogged arteries (in their neck or heart, for example), often report no serious symptoms until the arteries are almost completely blocked (that is. the last little increase in blockage causes major problems). Explain how information gleaned from this power function might shed light on this phenomenon. 2 Suppose that we are holding the flow rate constant and that we measure the pressure as 25N/m 2 when the length is 12m and the radius is 20cm. Find the pressure if the radius increases to 30cm. (Note that the units on the radius are cm and not m.) Under the same conditions as in the previous part, what do we need to make the radius of the tube (in cm) if we can apply a maximum of 3.5N/m 2 of pressure to the fluid?

Explanation / Answer

a)http://medical-dictionary.thefreedictionary.com/Hagen-Poiseuille+law e) Q is proportional to L. Q is inversely proportional to R^4

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