Calculating Angle for Water Rolling on Glass Plane

[Winzer]

Homework Statement

So I need to get a rough calculation:
At what angle does drops of water start rolling down a plane of glalss.
This is for my project where we are using a solar still to purify water. I just need ot get a rough calculation so I know at what angle to tilt the plane of glass. I am aware that I could experiment but for the class I need calculations.
Thanks.

 

[mgb_phys]

Surface tension is what is stopping the drops from moving.
You will need to investigate what parameters effect the surface tension - this is going to be dominated by the nature of the glass surfacd, how smooth, what type of glass (surface charge) and any impurities on the surface ( particulalry detergents).

There isn't a single number for just glass.

 

[m2003]

I would approach this problem by first considering the forces acting on the water droplets on the glass plane. The main force at play is gravity, which is pulling the droplets downwards. However, there is also a frictional force between the water droplets and the glass surface, which is resisting the droplets from sliding down the plane.

To determine the angle at which the droplets will start to roll down the plane, we need to find the point at which the frictional force equals the component of gravity pulling the droplets down the plane. This can be calculated using the formula Ff = μmgcosθ, where Ff is the frictional force, μ is the coefficient of friction between water and glass, m is the mass of the water droplet, g is the acceleration due to gravity, and θ is the angle of the plane.

We can rearrange this equation to solve for θ, giving us θ = arccos(Ff/μmg). The value of μ for water on glass is typically around 0.1, and the mass of a water droplet can be estimated based on its volume and density. Therefore, by plugging in these values and the desired frictional force, we can calculate the angle at which the droplets will start to roll down the glass plane.

However, it is important to note that this calculation will only give us an approximate angle, as there are other factors that may affect the actual angle at which the droplets start to roll, such as the surface roughness of the glass, the size and shape of the droplets, and any external forces acting on the droplets. Therefore, it may be necessary to conduct experiments to determine the most effective angle for your specific solar still project.