K factors describe a fitting's shape. A control valve gets a different treatment entirely, because valve makers sell capacity, and capacity is defined by a test, not by a theory.

The metric form is $Q = K_v \sqrt{\dfrac{\Delta p}{SG}}$ — Q equals K-v root delta-p over S G. $Q$ is the flow in cubic metres per hour, $\Delta p$ the pressure drop across the valve in bar, and $SG$ the specific gravity of the fluid, a bare ratio against water (1.00 for water, about 1.05 for 30% glycol, 1.44 for a heavy calcium-chloride brine). $K_v$ is the flow coefficient, and its definition is the whole trick: the m³/h of water the valve passes at exactly 1 bar of drop. It is not dimensionless and it is not a ratio — it is a measured flow, wearing the units it was measured in.

The US original is $C_v$, defined the same way in the other currency: the gallons per minute of 60 °F water at 1 psi of drop. The two are the same idea and convert as $C_v \approx 1.156\,K_v$. Neither number means anything without knowing which convention it came from, so catalogues that print a bare number and no units have told you nothing.

The square root is where the intuition lives. Flow follows the root of the drop: quadruple the pressure across a valve and you get only twice the flow. Run that backwards and it is more sobering — asking a valve for twice its comfortable flow costs four times the pressure drop, which is how a control valve ends up eating the entire pump curve.

And $SG$ sits under the root, dividing. A heavier fluid passes LESS through the same valve at the same drop: a brine at $SG = 1.44$ has a root of 1.2, so it flows a sixth less than water would. On a glycol loop the derate is small and real, and it is the first thing to check when a balanced system will not reach its numbers.