Jean-Louis-Marie Poiseuille was a french physician who invented an superior method for measuring blood pressure. He also studied how liquid flowed through tubes. He found that rate of flow depended on the diameter and length of the tube and pressure difference between the end. He formulated an equation called Poisuille‘s law, which describes the relationship. The unit of viscosity (resistance to flow) is named the poise in his honor. The viscosity of a fluid can be defined as the measure of how resistive the fluid is to flow. It is the same as the friction of solid bodies because it also serves as a mechanics for transforming kinetic energy into thermal energy. Poise are cgs unit of dynamic viscosity, equal to 1 g cm-1 s-1, 1/10 Pa
Blood vessels are shaped like cylindrical tubes with a length L and a radius R. The velocity v of the blood reaches it’s maximum all along the central axis of the tube. The velocity of the blood decreases as the distance r from the axis increases until v becomes zero at the wall, because of friction at the walls of the tube. In 1840 Jean-Louis-Marie Poiseuille discovered the relationship between v and r and called it the law of laminar flow.
This law states that:
v = (P/4nL)(R^2-r^2) If P and L are constant, than v is a function of r with a domain of [0,R]
The law of laminar flow requires you to know how to use basic arithmetic, and exponential functions. We can also use the law of laminar flow to find the velocity gradient, which is the instantaneous rate of change of velocity with respect to r. To find the velocity gradient you must know how to find derivatives. You must also know that if y = f(x) then the derivative dy/dx can be interpreted as the rate of change of y with respect to x.
(For the following equations: x1 stands for x with a subscript of 1 and x2 stands for x with a subscript of 2)
You must also know that the change in x = x2 - x1
this implies that the change in y = f(x2) - f(x1)
So, the difference quotient equals the difference in y divided by the difference in x = [(x2) - f(x1)] / (x2 - x1)
And the difference quotient is the average rate of change of y with respect to x over the interval [x1,x2].
The limit as the change in x goes to zero is the derivative of x1, which can be interpreted as the instantaneous rate of change of y with respect to x.
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