Explanation:
Apply the mass of balance as follows.
Rate of accumulation of water within the tank = rate of mass of water entering the tank - rate of mass of water releasing from the tank
[/tex]\frac{dh}{dt} + \frac{0.01}{0.01}h[/tex] =
+ h = 1
= 1 - h
= dt
= t + C
Given at t = 0 and V = 0
= 0
or, h = 0
-ln(1 - h) = t + C
Initial condition is -ln(1) = 0 + C
C = 0
So, -ln(1 - h) = t
or, t = ........... (1)
(a) Using equation (1) calculate time to fill the tank up to 0.6 meter from the bottom as follows.
t =
t =
=
= 0.916 seconds
(b) As maximum height of water level in the tank is achieved at steady state that is, t = .
1 - h = exp (-t)
1 - h = 0
h = 1
Hence, we can conclude that the tank cannot be filled up to 2 meters as maximum height achieved is 1 meter.
