# Thread: Is this equaion dimensionally homogenous?

1. ## 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:

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

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

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

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

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

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

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

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?