4. The compliance C (also called capacitance) of a thin-walled cylindrical pressure is the change of volume V with change of pressure P. That is: C = πr³ Lo dv dp' a. Show that C = (2.52v), if the tubing has length Lo, radius ro, thickness to, Young's Eto modulus E, and Poisson ratio v. Assume small deformations and ro » to, and incompressible fluid. Hints: 1) This means you need to find an equation for V in terms of P, where V is the volume of the cylindrical lumen at a pressure P. Once you get V(P), take the derivative to get C = dV/dP. 2) For help calculating Volume V, see the example problem in lecture 15, that calculates the volume of a pressurized spherical vessel, but here you have a cylindrical vessel, and you are calculating dV/dP not AV/Vo. b. The Thomas lab wants to control the response time RC, of fluidic circuits used to study the effect of pulsatile flow on cell adhesion. Assume that the tubing is the major source of resistance πr³ Lo in the circuit, so R = 18, and of capacitance, so C = (2.5 2v), so RC is the product of Eto these expressions. How could you change your tubing to decrease the time constant RC? That is, when you are choosing tubing for your experiment, how should you pick between different tubing sizes or materials? E.g. would it help to change ro by picking narrower or wider tubing? What else?
4. The compliance C (also called capacitance) of a thin-walled cylindrical pressure is the change of volume V with change of pressure P. That is: C = πr³ Lo dv dp' a. Show that C = (2.52v), if the tubing has length Lo, radius ro, thickness to, Young's Eto modulus E, and Poisson ratio v. Assume small deformations and ro » to, and incompressible fluid. Hints: 1) This means you need to find an equation for V in terms of P, where V is the volume of the cylindrical lumen at a pressure P. Once you get V(P), take the derivative to get C = dV/dP. 2) For help calculating Volume V, see the example problem in lecture 15, that calculates the volume of a pressurized spherical vessel, but here you have a cylindrical vessel, and you are calculating dV/dP not AV/Vo. b. The Thomas lab wants to control the response time RC, of fluidic circuits used to study the effect of pulsatile flow on cell adhesion. Assume that the tubing is the major source of resistance πr³ Lo in the circuit, so R = 18, and of capacitance, so C = (2.5 2v), so RC is the product of Eto these expressions. How could you change your tubing to decrease the time constant RC? That is, when you are choosing tubing for your experiment, how should you pick between different tubing sizes or materials? E.g. would it help to change ro by picking narrower or wider tubing? What else?
Human Physiology: From Cells to Systems (MindTap Course List)
9th Edition
ISBN:9781285866932
Author:Lauralee Sherwood
Publisher:Lauralee Sherwood
Chapter11: The Blood
Section: Chapter Questions
Problem 1SQE
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Please help and explain homework
Transcribed Image Text:4. The compliance C (also called capacitance) of a thin-walled cylindrical pressure is the change of
volume V with change of pressure P. That is: C =
πr³ Lo
dv
dp'
a. Show that C = (2.52v), if the tubing has length Lo, radius ro, thickness to, Young's
Eto
modulus E, and Poisson ratio v. Assume small deformations and ro » to, and incompressible
fluid. Hints: 1) This means you need to find an equation for V in terms of P, where V is the volume of the
cylindrical lumen at a pressure P. Once you get V(P), take the derivative to get C = dV/dP. 2) For help
calculating Volume V, see the example problem in lecture 15, that calculates the volume of a pressurized
spherical vessel, but here you have a cylindrical vessel, and you are calculating dV/dP not AV/Vo.
b. The Thomas lab wants to control the response time RC, of fluidic circuits used to study the
effect of pulsatile flow on cell adhesion. Assume that the tubing is the major source of resistance
πr³ Lo
in the circuit, so R = 18, and of capacitance, so C = (2.5 2v), so RC is the product of
Eto
these expressions. How could you change your tubing to decrease the time constant RC? That is,
when you are choosing tubing for your experiment, how should you pick between different tubing sizes or
materials? E.g. would it help to change ro by picking narrower or wider tubing? What else?
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