Im having problems figuring out what formulas I\'m suppose to put into Excel and
ID: 1857087 • Letter: I
Question
Im having problems figuring out what formulas I'm suppose to put into Excel and how to set it up.I have an x, y, dy/dx, and new y column. The time step is 0.1s and I need from 0 to 6 seconds.
Consider a cylindrical tank of radius 0.25 m initially containing water up to 0.25 m high from the bottom. The plug is pulled from a circular hole (radius 0.05 m) at the bottom of the tank.
If you were to apply Bernoulli equation from the hole at the bottom of the tank to the top of the water surface, you would show that the velocity of water draining through the hole at the bottom of the tank would be:
where V = velocity, g = gravity and y = water level in the tank. NOTE: The water level in the tank is time dependent, y(t), and hence, the velocity is time dependent, V(t).
Conservation of mass means that the volumetric drainage rate within the tank must be equal to the flow volume draining through the hole:
where rtank and rhole are the radii of the tank and hole, respectively, y is the water level in the tank, t is time and g is gravity.
Using separation variables, the analytical solution is found to be:
where y = water level in the tank, y0 = initial water level in the tank, rhole and rtank are the radii of the hole and tank, respectively, g = gravity and t = time.
Im having problems figuring out what formulas I'm suppose to put into Excel and how to set it up.I have an x, y, dy/dx, and new y column. The time step is 0.1s and I need from 0 to 6 seconds.
Consider a cylindrical tank of radius 0.25 m initially containing water up to 0.25 m high from the bottom. The plug is pulled from a circular hole (radius 0.05 m) at the bottom of the tank.
If you were to apply Bernoulli equation from the hole at the bottom of the tank to the top of the water surface, you would show that the velocity of water draining through the hole at the bottom of the tank would be:
where V = velocity, g = gravity and y = water level in the tank. NOTE: The water level in the tank is time dependent, y(t), and hence, the velocity is time dependent, V(t).
Conservation of mass means that the volumetric drainage rate within the tank must be equal to the flow volume draining through the hole:
where rtank and rhole are the radii of the tank and hole, respectively, y is the water level in the tank, t is time and g is gravity.
ANALYTICAL SOLUTION:
Using separation variables, the analytical solution is found to be:
where y = water level in the tank, y0 = initial water level in the tank, rhole and rtank are the radii of the hole and tank, respectively, g = gravity and t = time.
Explanation / Answer
https://docs.google.com/viewer?a=v&q=cache:TkX68RH0bzMJ:www.mathcs.richmond.edu/~jad/232s07/Euler_Lab3.pdf+&hl=en&gl=in&pid=bl&srcid=ADGEEShYYxUdXOUVndyJ1_XnOyclbvIejmwUUgv0B496MKdZ4XYDjKRlrf68-t3mjkRAwApq5XTMJ32HTBVBbgcGGI3YnzV0bfvEYCRuUwGse9qytQD7Rc45tDxRFspbP5UQt8MTgzxw&sig=AHIEtbSdhiy9reUD-Y9VsTmM6n-ZzQUO5w
http://www2.seminolestate.edu/lvosbury/DiffEq_Folder/ExamplesNumMeth.htm
Euler's method is a simple one-step method used for solving ODEs. In Euler