Answer
$K_{v}\ a n d\ K_{u}$ are dimensionless
the equation is general homogeneous so it will be valid for any system of units
Work Step by Step
$\begin{aligned} & \Delta p=k_v \frac{\mu V}{D}+K_u\left[\frac{A_0}{A_1}-1\right]^2 \rho v^2 \\ & {\left[F L^{-2}\right] \doteq\left[K_v\right]\left[\left(\frac{F T}{L^2}\right)\left(\frac{L}{T}\right)\left(\frac{1}{L}\right)\right]+\left[K_u\right]\left[\frac{\left(L^2\right)}{\left(L^2\right)}-1\right]^2\left[\frac{F T^2}{L^4}\right]\left[\frac{L}{T}\right]^2} \\ & {\left[F L^{-2}\right] \doteq\left[K_v\right]\left[F L^{-2}\right]+\left[K_u\right]\left[F L^{-2}\right]}\end{aligned}$
$K_{v}\ a n d\ K_{u}$ are dimensionless because each term must have the same dimension .
the equation is general homogeneous so it will be valid for any system of units
