Buoyancy fluxes in a stratififed fluid and units

Question

I am calculating the buoyancy flux ($B$) for a stratified fluid as follows: $$ B=\frac{g\alpha S}{C_{pw}\rho_0} $$

where $g = 9.81$ $m/s$; $\alpha = 1.6 t\times10^{-5} + 9.6\times10^{-6} \times (20 \text{ degC})$; $S = 100\text{ }Wm^{-2}$, $\rho_0 = 1000$ $kg/m^3$, and $C_{pw}$ is the specific heat of water.

The question I have is: Is $C{pw} = 4200$ or $4.2$ I've seen it used both ways, and I am unsure which I would use with the units of the other terms in the equation.

Answer 1

You are using standard SI units for all the other terms (no unit multipliers). If you look at the specific heat of water (at standard atmospheric pressure) you will find the specific heat is $\approx 4.2 \mathrm{kJ\,kg^{-1}\,K^{-1}}$ or $\approx 4200 \mathrm{J\,kg^{-1}\,K^{-1}}$. It is the latter you want to use.

I hope this helps.