This question talks about the head loss coefficient for a valve, i.e., $K_{L}$ for $h_{L} = K_{L} V^{2} / 2g$ where $h_{L}$ is head loss.

First, head loss coefficient for a valve with respect to the open position is generally provided as a table.
e.g. head loss coefficient for a gate valve

Second, Darcy friction factor of Darch-Weisbach equation for a pipe flow is generally provided as Moody chart.
There are many emprical equations for Darcy friction factor.
e.g. $1/\sqrt{f} = -1.8 \log \left [ \left ( \varepsilon / D /3.7 \right )^{1.11} + 6.9 / \text{Re} \right ]$

Here is the question.

General method to consider both the Darcy friction factor and valve head loss coeffient for a pipe flow head loss is plain addition: each head loss is considered as a major or minor loss term.

However, because the flow that passes through the valve is also a pipe flow, the head loss coefficient for a valve would be also affected by the flow rate (flow speed).

This effect with respect to the flowrate may be very small compared to the effect of the valve open position; however, I want to know if there is any table, chart, or experimental result that presents this change in valve head loss coefficient.