If I go for a walk at, say 4 km/hour, unless there is a breeze blowing, I probably won't notice the air around me at all. If I go for a swim though, I will immediately notice the viscosity of the water and the effort needed to move through it.
On that sort of scale, I wonder is it possible to estimate how normal still air applies in terms of viscosity, to a mosquito or other similar sized insect, utilising standard fluid dynamics techniques?
I don't wish to ask a biology based question, or how any insect actually flies, which can be found at Insect Flight. This article implies that insect flight is still a subject of active investigation.
The range of Reynolds number in insect flight is about 10 to $10^4$, which lies in between the two limits that are convenient for theories: inviscid steady flows around an airfoil and Stokes flow experienced by a swimming bacterium. For this reason, this intermediate range is not well understood.
Instead I wonder do we know, compared to the human experience with respect to the fluid viscosity difference between still air and water, what air "feels" like to move through for an insect, such as a mosquito?
In other words, is it possible to scale up the insect flying "experience" to the human level, and get an idea of what the human equivalent of the viscosity involved is? I appreciate it may be impossible to answer this question without referring back to the flight dynamics of insects, in which case my apologies as there may be no current answer.
Best Answer
What you need to compare when looking at bodies of different sizes and asking how the forces relate, is in general, the Reynolds Number as you included in your question. This is defined as:
$$ Re = \frac{u L}{\nu} $$
where $u$ is the fluid velocity, $L$ is a representative length scale and $\nu$ is the kinematic viscosity of the fluid. This can also be thought of as the ratio of the inertial forces to the viscous forces. So, when this number is small, the viscous forces dominate and when it is large, the inertial forces dominate.
The hardest part is picking an $L$. In this case though, it's not so bad. Let's assume that a mosquito is approximately a sphere. Adults rarely exceed 16mm in length, so let's just approximate and say they are 10mm long, so as a sphere they would have a radius of 5mm. Let's then take a normal day at standard temperature and pressure (STP) so that the kinematic viscosity of air is $\nu = 15.11e-6$. And let's assume a light breeze, say 5 m/s. This gives us a Reynolds number of (which hey, also matches the range you posted -- good start!):
$$ Re = \frac{u L}{\nu} = \frac{5 \times 0.005}{15.11e-6} \approx 1655 $$
Okay, so now if we want a human to feel the same inertial-to-viscous force ratio, we want to keep the Reynolds number the same. We can pretend a human is a cylinder. And we can further say that an average human is, roughly, 0.4 meters wide which would give a radius of 0.2 meters. We'll assume the Reynolds number is the same and the air viscosity is the same and solve for a wind velocity to give a similar feel:
$$ u = \frac{\nu Re}{L} = \frac{15.11e-6 \times 1655}{0.2} \approx 0.12 m/s$$
Counter-intuitive maybe, but what we're considering here is what velocities are required to feel the same ratio of inertial to viscous forces.
In this case, we altered the wind speed but we could also alter the viscosity. If we wanted to do that, let's say we held the speed the same, we would get:
$$ \nu = \frac{u L}{Re} = \frac{5 \times 0.2}{1655} \approx 0.0006 m^2/s$$
This number is almost 40 times larger than the viscosity of air. This means that for a human to feel an equivalent set of forces, they would have to be in a 5 m/s flow of something like hot asphalt, SAE 150 gear oil or diesel fuel. None of which sounds very pleasant, but honestly neither does flying around as a mosquito.