Hi,
I am just thinking out loud, but I believe that I am on the right track.
As the plate rotates around the thread, three different forces are exerted on it:
1) Force from the string
2) Gravity
3) Centrifugal force
The second force will force some parts of the plate to spin faster than some...
You made one mistake: You wrote W*m^2*s*kg*K/m^2*kg*J = W*s*K/J
On the left hand side you have W*j, but on the right hand side you have W/j. How did you do that?
Also, your second eqn should be
q = A* k * (T outside - T water) / l
so that q has units of W (or j/s), although, that is not really...
Out of curiosity, how would you solve the problem with the ice. The ice is a solid undeformable material. As the beaker moves, the ice would stay still. So, how would you solve for the angle?
Because P is a function of x, z. Therefore, you can write that
dP=(dp/dx)*dx+(dP/dz)*dz
Why does the negative sign bother you?
The above eqn simplifies as follows:
1=(a*rho)dx+(-g*rho)*dz
Therefore, the slope is dz/dx=a/g=tan(theta)
You are a little bit confused, and I do not know how to help you.
Lets start with the eqn P=-rho * g * h + const
What is the meaning of this eqn? It simple related the pressure to the depth. Nothing more than that!
Similarly, dP/dz=-rho*g relates the pressure slope to gravity force...
As I said, this equation is not derived from Bernoullis' equation. So you do not need to differentiate with respect to P.
Actually, you are right, You need to take a force balance. Are you familiar with the Navier-Stokes equation? This equation is an extension to Bernoullis' equation, when...
Hi Delzac,
I did not understand your second question.
First of all, the equation dP/dz=-g*rho is not derived from Bernoulli's equation. Bernoullis' equation states that P/rho+g*z+v*2=const.
You may consider the equation dP/dz=-g*rho as a constitutive equation. It simply says that as we move...
This is correct!
One thing that I missed is that in the 2nd eqn you have the term "k/l". This term has the units of "h", and some people do suggest to set "h=k/l". So, the 2nd eqn is OK.
When you write an eqn make sure that the units are in balance.
Your first eqn is wrong:
Tf - Ti = q * A /...
Actually, I do not do any kind of projection. All the points are close to each other, and I could assume that they have the same z. I believe that z is important when you go from one hemisphere to the other. Otherwise, you won't find two different points on the surface of a sphere that have the...
I just realized that I am trying to compare the solution from two different coordinate systems. The only thing I could compare is the distance between two points, but even that would not be the same, due to the enormous radius of the planet.
I hope I am posting in the right section.
Up to today I was assuming that Earth is a sphere, and I was using the spherical coordinates to convert longitude/latitude to x/y. But, I wanted to use a more accurate transformation, and I wanted to calculate x/y by considering the actual shape of the...
P is the pressure
I made a typo, a*rho=F*rho/m
You could set b.c., but it would not change the slope.
Remember, that the pressure at the water surface is constant, and equal to 1atm.