Calculate the pressure drop per cm along the aorta using the data of Example 10–12 and Table 10–3.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The volume rate of flow through the tube is gonna be given by Poiseuille's equation, π times radius to the power of 4 times the pressure difference divided by 8 times the viscosity of the blood times the length of the aorta and then we'll solve this for P 1 minus P 2 over l that will be the pressure difference per length— pascals per centimeter is what we are gonna work it out to— and we'll multiply both sides then by 8 times η divided by π times R to the 4 and then we get the pressure difference per length is 8 times viscosity times volume rate of flow divided by π times radius to the power of 4 and this is gonna give us units of pascals per meter and so we have to convert those meters into centimeters so multiply by 1 meter for every 100 centimeters and that will be pascals per centimeter. Volume rate of flow is the cross-sectional area of the aorta times the speed of the blood flow and that's gonna be πr squared times v so we substitute that in for Q and we have π's canceling here and R squared on the top cancels with two of the R's on the bottom leaving us with the pressure difference per length is 8 times η times v over R squared times this conversion factor. So that's 8 times 4 times 10 to the minus 3 pascal seconds— viscosity—times 40 times 10 to the minus 2 meters per second— speed of the blood— divided by 1.2 times 10 to the minus 2 meters— radius of the aorta—squared times 1 over 100 and that gives 0.89 pascals per centimeter pressure difference per length.