- #1
uniidiot
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Homework Statement
A tank is in a shape of a cylinder with a circular cross-section of area A. Initially the depth of water in the tank (the head) is h0. At time t = 0 water is allowed to leave the tank ffrom a valve at the bottom. The rate at which the water leaves the tank is proportional to the head of the water at that instant; the constant of proportionality, k, is related to the discharge coefficient or the tank.
Derive an expression for the head of water in the tank at any time t after it is allowed to empty.
How long does it take for the tank to lose 1/2 its water? How long does it take for the tank to empty.
Homework Equations
Code:
dy/dx = -ky
y = Ce^(-kt)
The Attempt at a Solution
dh/dt = -k(h - h0)
h(time) = (h - h0)e^(-kt)
ln ((h - h0) / h(time)) = kt
and this is where i get stuck that's even if I've got the first bit right?
any help would be great!
:)