My Math Forum centrifugal force on water in a glass

 Physics Physics Forum

 January 28th, 2017, 02:57 PM #1 Member   Joined: Oct 2016 From: Slovenia, Europe Posts: 52 Thanks: 5 centrifugal force on water in a glass 1. The problem statement, all variables and given/known data There is a cyllindrical glass (r=0.05 m) full of water. It is rotating around its vertical geometric axis with 3 turns per second. How many centimetres higher is water at the rim than in the centre of the glass . Water rotates together with the glass. 2. Relevant equations p=ρah ω=2πγ a=ω2r 3. The attempt at a solution All I know is that the shape of water is parabolic. In the centre there is no additional pressure from rotation, the pressure on the glass is p=ρah, a=ω2r total pressure on any point is px + py (vectorial sumation)
 January 29th, 2017, 03:28 AM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,833 Thanks: 649 Math Focus: Yet to find out.
 January 29th, 2017, 03:37 AM #3 Member   Joined: Oct 2016 From: Slovenia, Europe Posts: 52 Thanks: 5 nobody really helped me there, so i asked here too
 January 29th, 2017, 03:47 AM #4 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,833 Thanks: 649 Math Focus: Yet to find out. But you only posted 12 hours ago . But fair enough. Just whatever has been posted there may be of help to someone here.
 January 29th, 2017, 05:55 AM #5 Member   Joined: Oct 2016 From: Slovenia, Europe Posts: 52 Thanks: 5 Joppy, you do not know the answer?
January 29th, 2017, 05:59 AM   #6
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,833
Thanks: 649

Math Focus: Yet to find out.
Quote:
 Originally Posted by srecko Joppy, you do not know the answer?
I do not.

 January 29th, 2017, 08:22 AM #7 Math Team     Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 Been a long time since I've dealt with fluid mechanics, but here is a go at it ... Referencing the diagram, the red dot represents a fluid particle on the surface of mass $m$. The free body diagram to the right is a representation of the forces acting on that particle with the blue line representing a line tangent to the curve formed by the fluid surface. fluid particle is in translational equilibrium ... $F_c = mr \omega^2 = N\sin{\theta}$ $mg = N\cos{\theta}$ $\dfrac{N\sin{\theta}}{N\cos{\theta}} = \dfrac{mr\omega^2}{mg}$ $\tan{\theta} = \dfrac{r \omega^2}{g}$ since $r = x$ from the coordinate system ... $\tan{\theta} = \dfrac{x \omega^2}{g}$ slope of the tangent line, $\tan{\theta} = \dfrac{dy}{dx}$ ... $\dfrac{dy}{dx} = \dfrac{x \omega^2}{g} \implies y = \dfrac{x^2 \omega^2}{2g}$ sub in the radius of the cylinder for $x$ and $\omega = 6\pi \, rad/sec$ to determine $y$. Thanks from topsquark and srecko
 January 29th, 2017, 08:31 AM #8 Member   Joined: Oct 2016 From: Slovenia, Europe Posts: 52 Thanks: 5 The shape of water is not a parabola then???
January 29th, 2017, 08:55 AM   #9
Math Team

Joined: Jul 2011
From: Texas

Posts: 3,002
Thanks: 1587

Quote:
 Originally Posted by srecko The shape of water is not a parabola then???

yes ... look again at the equation for $y$

$y = kx^2$ where $k = \dfrac{\omega^2}{2g}$

 January 29th, 2017, 11:23 AM #10 Member   Joined: Oct 2016 From: Slovenia, Europe Posts: 52 Thanks: 5 ok, i got it. Thanks for your effort. This forum is really helpful

 Tags centrifugal, force, glass, water

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Ganesh Ujwal Physics 2 January 3rd, 2015 06:47 AM leo255 Calculus 1 December 16th, 2014 07:48 PM tinyone Physics 6 March 23rd, 2011 01:20 AM deadmandx Physics 3 December 4th, 2008 02:36 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top