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Math Help - application of integration

  1. #1
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    application of integration

    in a cylindrical tube of radius R and length l, the velocity v of the fluid flowing through the tube depends upon the distance r from the central axis according to:

    v(r) = (P / (4nl)) * (R^2 - r^2) , for 0<=r<=R

    where P is the pressure difference between the ends of the tube
    and n is the fluid viscosity

    compare the average velocity with the maximum velocity over 0<=r<=R

    the answer i got for average velocity was (PR^2) / (6nl)
    and for maximum velocity was (PR^2) / 4nl

    can someone verify if these are the correct answers and if not provide details on the correct solution

    thanks in advance
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  2. #2
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    Quote Originally Posted by razorfever View Post
    in a cylindrical tube of radius R and length l, the velocity v of the fluid flowing through the tube depends upon the distance r from the central axis according to:

    v(r) = (P / (4nl)) * (R^2 - r^2) , for 0<=r<=R

    where P is the pressure difference between the ends of the tube
    and n is the fluid viscosity

    compare the average velocity with the maximum velocity over 0<=r<=R

    the answer i got for average velocity was (PR^2) / (6nl)
    and for maximum velocity was (PR^2) / 4nl

    can someone verify if these are the correct answers and if not provide details on the correct solution

    thanks in advance
    both look fine to me ...

    v_{avg} = \frac{P}{4Rnl} \int_0^R R^2 - r^2 \, dr = \frac{PR^2}{6nl}

    v_{max} occurs when r = 0 ... v(0) = \frac{PR^2}{4nl}
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  3. #3
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    thanks ... this was my first time attempting this sort of example and i wasn't sure if it was correct ... but now i know
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