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Math Help - Poiseuille's law?

  1. #1
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    Poiseuille's law?

    Poiseuille's law describes the velocities of fluids flowing in a tubeófor example, the flow of blood in a vein. This law applies when the velocities are not too largeómore specifically, when the flow has no turbulence. In this case the flow is laminar, which means that the paths of the flow are all parallel to the tube walls. The law states that v=k(R^2-r^2), where v is the velocity, k is a constant (which depends on the fluid, the tube, and the units used for measurement), R is the radius of the tube, and r is the distance from the centerline of the tube. Since k and R are fixed for any application, v is a function of r alone, and the formula gives the velocity at a point of distance r from the centerline of the tube

    (a) What is r for a point along the walls of the tube?

    (In so many words, this basicly means to get r by itself, right?)

    (b) What is the velocity of the fluid along the walls of the tube?

    (...Wait, it didn't give me a value? I'm going to take a wild guess and say the fluid along the wall is zero.)
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  2. #2
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    Hello MathBane
    Quote Originally Posted by MathBane View Post
    Poiseuille's law describes the velocities of fluids flowing in a tubeófor example, the flow of blood in a vein. This law applies when the velocities are not too largeómore specifically, when the flow has no turbulence. In this case the flow is laminar, which means that the paths of the flow are all parallel to the tube walls. The law states that v=k(R^2-r^2), where v is the velocity, k is a constant (which depends on the fluid, the tube, and the units used for measurement), R is the radius of the tube, and r is the distance from the centerline of the tube. Since k and R are fixed for any application, v is a function of r alone, and the formula gives the velocity at a point of distance r from the centerline of the tube

    (a) What is r for a point along the walls of the tube?

    (In so many words, this basicly means to get r by itself, right?)

    (b) What is the velocity of the fluid along the walls of the tube?

    (...Wait, it didn't give me a value? I'm going to take a wild guess and say the fluid along the wall is zero.)
    (a) Read the question carefully. r is the distance from the centre of the tube. The radius of the tube is R. So along the walls of the tube, r = R.

    (b) You're right. When r = R,\; v = 0.

    Grandad
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