4. The speed of blood flow in an artery is given by Poiseuille’s law. The law says that blood flow is fastest in thecenter of the artery and slower at the edges. We can express this asS(r) =C(R2−r2).In this equationRis the fixed radius of the artery andSis the blood flow speed at a distancerfrom the centerof the artery. In a typical human aortaR= 1.4 centimeters and the peak blood flow velocity is 90 centimetersper second.(a) Calculate the constantC.1
Question
- The speed of blood flow in an artery is given by Poiseuille’s law. The law says that blood flow is fastest in thecenter of the artery and slower at the edges. We can express this asS(r) =C(R2−r2).In this equationRis the fixed radius of the artery andSis the blood flow speed at a distancerfrom the centerof the artery. In a typical human aortaR= 1.4 centimeters and the peak blood flow velocity is 90 centimetersper second.(a) Calculate the constantC.1
Solution
To calculate the constant C, we need to use the given values of S, R, and r in the equation S(r) = C(R^2 - r^2).
Given that the peak blood flow velocity (S) is 90 cm/s, this occurs at the center of the artery where r = 0. Also, the radius of the artery (R) is given as 1.4 cm.
Substituting these values into the equation gives:
90 = C(1.4^2 - 0)
This simplifies to:
90 = C(1.96)
To solve for C, divide both sides of the equation by 1.96:
C = 90 / 1.96
C = 45.92 cm/s
So, the constant C in Poiseuille’s law for the given conditions is approximately 45.92 cm/s.
Similar Questions
Assume that the average human aorta has a radius of 1 cm. The blood flow rate is approximately 84 cm3/s . What is the velocity of blood flow in cm/s?
Poiseuille’s Law describes the pressure drop in an artery of length L and radius r due to the viscosity of blood, where η is the coefficient of viscosity for the fluid and Q is the volume flow rate. According to Poiseuille’s Law, pressure drop would be MOST affected by:A.increasing the coefficient of viscosity by a factor of two.B.increasing the volume flow rate by a factor of two.C.increasing length of the artery by a factor of two.D.reducing the radius of the artery by a factor of two.
Poiseuille's Law describes flow rate through a cylinder. Which of the following statments is correct?Question 5Select one:a.Poiseuille's Law applies to laminar flow.b.Poiseuille's Law only applies in the absence of friction.c.Poiseuille's Law applies to a tube with varying radius.d.The flow rate is proportional to the length of the tube.e.The liquid flows due to its weight, and the effect of the flow is to cause a pressure difference between the ends of the tube.
Select the correct statement about blood flow. It is greatest where resistance is highest. Blood flow through the entire vascular system is equivalent to cardiac output. It is measured in mm Hg. It is relatively constant through all body organs. It reduces significantly with age.
1.4 litres of blood passes through an artery in 7 minutes. What is the rate of blood flow in millilitres per minute?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.