Water Circling Drain Coriolis effect

[ethopianprince]

Lets say a cone shaped funnel was made as I was draining water (due to coriolis effect) and that there is a given circumferential velocity (lets say its 5m/s) at a certain radius of the cone (lets say 15 cm), also the cone's vertex is inside the drain and is a certain distance (lets say this is 20 cm) from the drain. In this case how would one get to figuring out the flow rate at the start of the cone (at r=15cm) and at the vertex of the cone?

Just a situation I would like to know about IF it shows up on the Physics C test(s), you can never be too sure :P

 

[Simon Bridge]

Welcome to PF;
Leaving aside the coriolis effect for a bit, and the water thing, and just look at a simpler system to try to understand what is going on. How about an ice cone with a hockey-puck sliding down it? Then you can use your understanding of sliding on a slope with negligible friction.

If you just drop the puck, it slides right down.
If you give it a sideways push, you can make is spiral down.
Having to stay in contact with the cone wall puts a constraint on the angle of the spiral.
Because of the constricting circle, the speed around the spiral also increases.
To work it out you need to realize that energy, momentum and angular momentum are all conserved.

Water flow can be derived by considering a small volume of the water being like the puck and the coriolis effect adds an extra very small pseudoforce.

 

[ethopianprince]

So many things I don't want to think about at this hour -_- but thanks! a more step by step procedure would've been better but this way its better! thanks for your help!

Welcome to PF;
Leaving aside the coriolis effect for a bit, and the water thing, and just look at a simpler system to try to understand what is going on. How about an ice cone with a hockey-puck sliding down it? Then you can use your understanding of sliding on a slope with negligible friction.

If you just drop the puck, it slides right down.
If you give it a sideways push, you can make is spiral down.
Having to stay in contact with the cone wall puts a constraint on the angle of the spiral.
Because of the constricting circle, the speed around the spiral also increases.
To work it out you need to realize that energy, momentum and angular momentum are all conserved.

Water flow can be derived by considering a small volume of the water being like the puck and the coriolis effect adds an extra very small pseudoforce.

 

[Simon Bridge]

A step-by-step would be a "mindless walkthrough" ... you learn more this way.
What I'm hoping you'll see is that you already know the physics and the geometry to work it out as soon as the problem gets broken down.
So it's better to have a walkthrough in the sense it's easier and faster - but it is better this way for different and more meaningful reasons :)
Enjoy.

 

[ethopianprince]

Haha I will! just not today.. sleep>physics