Circular motion of water in a glass

[mavrick3987]

Hey all,

I'm attempting a lab where I want to have water moving in circular motion in a glass. I realized that the water will climb the side of the glass creating a sort of conical shape, if you will. I know that there is a way to calculate the change in height that occurs as the speed of the water increases. I was thinking centrifugal force, but I don't remember my motion well enough for this sort of thing.

Any and all help would be freakin' awesome

Aveld

 

[HallsofIvy]

The centripetal force necessary to hold something in a circle of radius R with constant speed v (and so angular speed $\omega$ is mv²/R or $m\omega^2R$. That vector force, <-mv²/R,0>, added to the gravitational force <0, -mg> gives total force m<-v²/R, -g>, in the xz-plane. More generally, it is [itex]m<-(v^2/R)cos(\theta), -(v^2/R)sin(\theta), -g>. It is the "equilibrium" condition, that that vector be perpendicular to the surface of the water that determines its form.

 

[ashishsinghal]

As I recall, It forms a paraboloid

 

[Andy Resnick]

Hey all,

I'm attempting a lab where I want to have water moving in circular motion in a glass. I realized that the water will climb the side of the glass creating a sort of conical shape, if you will. I know that there is a way to calculate the change in height that occurs as the speed of the water increases. I was thinking centrifugal force, but I don't remember my motion well enough for this sort of thing.

Any and all help would be freakin' awesome

Aveld

Are you rotating the glass, or are you moving the glass in orbital motion- moving the glass in a circle without rotating the glass? There's a big difference.

 

[PJC01]

Hello Aveld,

It sounds like you are trying to create a vortex or whirlpool effect in your glass of water. This is a common phenomenon that occurs when water is in circular motion. The water will indeed climb the sides of the glass due to centrifugal force, which is the outward force acting on an object in circular motion.

To calculate the change in height as the speed of the water increases, you can use the equation for centripetal force: Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the water, v is the velocity, and r is the radius of the circular motion. As the speed of the water increases, the centripetal force will also increase, causing the water to climb higher up the sides of the glass.

You can also calculate the velocity of the water at any given point using the equation v = ωr, where ω is the angular velocity and r is the radius. This can help you determine the speed at which the water is moving at different points in the circular motion.

I hope this helps with your lab. Good luck!