Differentisl equations math pronlem. Please show solution and will upvote . Graphs and tables should be produced with a computer. Include units where appropriate.
Overview : Fluid falls thru a cone and we wish to determine a function h(t) that models the level of the fluid in the cone t seconds after the process starts. We will divide the project into 4 parts: (1) The first part of the project is about constructing a first-order differential equation that h(t) must satisfy. (2) The second part of the project is devoted to solving the initial value problem to obtain the function h(t). (3) The third part of the project involves using a spreadsheet to compare the solution found in part 2 with actual measured data. (4) The last part of the project will include a method for improving the accuracy of the model.
Torricelli's Law: The exit velocity of the fluid at the hole in the bottom of a tank is the same as the velociy gained from a droplet released from a height h.
lole is r_(c)
(a) To simplify the geometry, we assume the shape of the funnel is a perfect cone with height H and radius R. With this simplification, the volume of the fluid in the funnel (cone) at a height h(t) and radius r(t) is given by:
V(t)=(pi )/(3)[r(t)]^(2)h(t)
Using similar triangles (or equivalent) eliminate r(t) from equation (1) so that the right hand side involves only h(t). Your answer should include R and H.Overview : Fluid falls thru a cone and we wish to determine a function h(t) that models the level of the fluid in the cone t seconds after the process starts. We will divide the project into 4 parts: (1) The first part of the project is about constructing a first-order differential equation that h(t) must satisfy. (2) The second part of the project is devoted to solving the initial value problem to obtain the function h(t). (3) The third part of the project involves using a spreadsheet to compare the solution found in part 2 with actual measured data. (4) The last part of the project will include a method for improving the accuracy of the model.
Torricelli's Law: The exit velocity of the fluid at the hole in the bottom of a tank is the same as the velociy gained from a droplet released from a height h.
hole is r_(c)
(a) To simplify the geometry, we assume the shape of the funnel is a perfect cone with height H and radius R. With this simplification, the volume of the fluid in the funnel (cone) at a height h(t) and radius r(t) is given by:
V(t)=(pi )/(3)[r(t)]^(2)h(t)
possible or use a word processor. Graphs and tables should be produced with a computer. Include units where appropriate. Overview : Fluid falls thru a cone and we wish to determine a function h(t) that models the level of the fluid in the cone t seconds after the process starts. We will divide the project into 4 parts: (1) The first part of the project is about constructing a first-order differential equation that h(t) must satisfy. (2) The second part of the project is devoted to solving the initial value problem to obtain the function h(t). (3) The third part of the project involves using a spreadsheet to compare the solution found in part 2 with actual measured data. (4) The last part of the project will include a method for improving the accuracy of the model.
R
t
Torricelli's Law: The exit velocity of the fluid at the hole in the bottom of a tank is the same the velociy gained from a droplet released from height h.
Hcm
h(t)
The radius of the hole is(re
1. (a) To simplify the geometry, we assume the shape of the funnel is a perfect cone with height H and radius R. With this simplification, the volume of the fluid in the funnel (cone) at a height h(t) and radius r(t) is given by: (1) V(t) = [r(t)]2 h(t) Using similar triangles (or equivalent) eliminate r(t) from equation (1) so that the right hand side involves only h(t). Your answer should include R and H
