What is the Reynold's number of a plate moving through a fluid? I read here that the equation of resistive drag $F = -bv$ can be used, assuming the particle is moving

through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, $R_{e}<1$)

In order to decide whether I can use $F = -bv$, I need to identify the Reynold's number of the rigid object I am working with.
In my case, I have a solid plate of width $w$, length $l$ and height $h$ which is moving perpendicular to the direction of the fluid at a velocity $v$. The fluid has a dynamic viscosity $μ$.
With the information mentioned above how can I calculate the Reynold's number of this rigid object?
 A: With the Reynolds Number:
$$\text{Re}=\frac{\rho v L}{\mu}$$
the characteristic length $L$ that can be used here is (e.g.):
$$L=\frac{l+h}{2}$$
assuming that $L \gg w$

Why is the formula for the characteristic length $L$ what you have
written it to be and why does $L$ need to be much bigger than $w$?

In many cases, the choice of a 'characteristic length' for the determination of $\text{Re}$ can be somewhat arbitrary and there's no 'hard and fast rule' to guide us. The case of a rectangular plate is such a case.
However, the point of transition from fully laminar to fully turbulent flow in terms of $\text{Re}$ number is not sharp. Here's Wikipedia's note on this:

For flow in a pipe of diameter $D$, experimental observations show that
for "fully developed" flow,[n 2] laminar flow occurs when $\text{Re}_D < 2300$
and turbulent flow occurs when $\text{Re}_D > 2900$. At the lower end of
this range, a continuous turbulent-flow will form, but only at a very
long distance from the inlet of the pipe. The flow in between will
begin to transition from laminar to turbulent and then back to laminar
at irregular intervals, called intermittent flow. This is due to the
different speeds and conditions of the fluid in different areas of the
pipe's cross-section, depending on other factors such as pipe
roughness and flow uniformity. Laminar flow tends to dominate in the
fast-moving center of the pipe while slower-moving turbulent flow
dominates near the wall. As the Reynolds number increases, the
continuous turbulent-flow moves closer to the inlet and the
intermittency in between increases, until the flow becomes fully
turbulent at $\text{Re}_D > 2900$. This result is generalized to
non-circular channels using the hydraulic diameter, allowing a
transition Reynolds number to be calculated for other shapes of
channel.

Because of this uncertainty on $\text{Re}$, some uncertainty on $L$ is not problematic. Without direct observation, whether flow will be laminar of turbulent will always be a bit of and 'educated guess'.
