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Thread: Is this equaion dimensionally homogenous?

  1. #1
    Super Member
    Dec 2008

    Is this equation dimensionally homogenous?

    The Fay-Riddel equation is, I gather, an equation that gives the heat flux through, for example, the nose-cone of a space vehicle during re-entry.

    I've been given a simplified version of this equation which looks as follows:

     \displaystyle q = k_h \sqrt{\frac{\rho}{R_n}} v^2

    From my understanding, these are the variables and their units:

     \displaystyle \text{ Heat flux, }q \, (W.m^{-2})

     \displaystyle \text{ Thermal Conductivity, }k_h \, (W.m^{-1}.K^{-1})

    \displaystyle \text{ Air Density, }\rho \, (kg.m^{-3})

    \displaystyle \text{ Radius of Curvature of Nose-cone, }R_n \, (m)

    \displaystyle \text{ Velocity, }v \, (m.s^{-1})

    Where m is metre, s is second, W is watt, K is kelvin, kg is kilogram.

    Clearly it can't be homogeneous because there's a kelvin on the RHS, and none on the LHS...

    Can anybody shed some light on this equation I've been given? Is it erroneous?
    Last edited by Mush; November 11th 2009 at 08:37 PM.
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