I have been reading through the Flow Simulation Technical Reference and found a series of equations to calculate the pressure drop. I have found two (2) equations that are quite useful (for anyone interested they are on page 45), however, one of the math functions used I have not seen before. I was hoping someone could explain it to me.

The first equation is: k= delta(P)*S/(m*L)

where:

delta(P) = The change of pressure

S = Cross-sectional Area

m = Mass flow rate

L = Length

This equations is fine, I can rearrange this to isolate delta(P). The second equation is to define k which is the porous medium resistance to fluid flow. The equation is:

k=-grad(P)/(rho*V)

where:
P = Fluid Pressure

rho = Fluid Density

V = Velocity of the fluid

I have not seen the 'grad' function before, so maybe someone explain tat to me. Also I would like to know the units of k,I'm assuming it has no units as its a coefficient (though I could be wrong) but I want to be able to prove that, please note I work in SI units. If it is easier for you to explain using the imperial units, please do so and I will convert the results. Thanks.