- #1
Marcos Domingues
- 2
- 0
Homework Statement
[/B]
I have this expression: dV/dt = F0 - K*h^(1/2); it describes a variation in time of a fluid volume V in a cone-shaped tank of total volume H*pi*R²/3;
By a trigonometric relation we get V = (pi*R²/3*H²)*h³; since tan a = H/R = h/r
where: R = radius of the tank; H = height of the tank; h = variable height of the fluid; r = radius related to a specific height h
So, when we replace V, we got the general expression (pi*R²/3*H²) d(h³)/dt = F0 - K*h^(1/2);
This d(h³) term is the main problem on the integration. How do I integrate this expression?
Homework Equations
(pi*R²/3*H²) d(h³)/dt = F0 - K*h^(1/2)
The Attempt at a Solution
Maybe consider d(h³) = dh*dh*dh and solve it as multiple integrals?
Last edited by a moderator: