1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Coordinate systems for divergence

  1. Mar 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Compute the divergence in cylindrical coordinates by transforming the expression for divergence in cartestian coordinates.

    2. Relevant equations

    F = F_x i + F_y j + F_z k
    div F = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z .......... (divergence in cartesian coordinates)

    I need to transform this into

    divF = (1/rho)(∂(rho*F_rho)/∂rho) + (1/rho)(∂F_theta/∂theta) + ∂F_z/∂z ...... (divergence in cylindrical coordinates)

    3. The attempt at a solution

    Using the chain rule,
    ∂F_x/∂x = (∂F_x/∂rho)(∂rho/∂x) + (∂F_x/∂theta)(∂theta/∂x) + (∂F_x/∂z)(∂z/∂x)
    ∂F_y/∂y = (∂F_y/∂rho)(∂rho/∂y) + (∂F_y/∂theta)(∂theta/∂y) + (∂F_y/∂z)(∂z/∂y)
    ∂F_z/∂z = (∂F_z/∂rho)(∂rho/∂z) + (∂F_z/∂theta)(∂theta/∂z) + (∂F_z/∂z)(∂z/∂z)

    ∂rho/∂x = x/∂ = costheta
    ∂theta/∂x = -y/rho^2 = -sintheta/rho
    ∂z/∂x = 0
    ∂rho/∂y = y/∂ = sintheta
    etc. (these are the transformational equations)

    Then I try inputing this into the cartesian definition for divergence and obtain
    divF = [(∂F_x/∂rho)costheta + (∂F_x/∂theta)(-sintheta/rho)] + [(∂F_y/∂rho)sintheta + (∂F_y/∂theta)(costheta/rho)] + ∂F_z/∂z

    But how does that simplify to the expression in cylindrical coordinates?
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted