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flow rate/volume/drain rate
- Thread starter ndnd
- Start date
D
Deleted member 4993
Guest
How would I figure the time it would take to drain/fill a tank when there is a rate at which it is draining that depends on the volume in the tank which is also changing at a certain rate due to flow into the tank?
Using calculus, set up differential equation and solve....
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,760
If V(t) is the volume at time t, \(\displaystyle \alpha(V)\) is the rate, depending upon the volume, at which the tank drains, and \(\displaystyle beta\) is the rate at which the tank is being filled, then
\(\displaystyle \frac{dV}{dt}= \beta- \alpha(V)\).
Without knowing more about how the rate at which the tank drains "depends on the volume", we cannot say more. If the rate at which the tank drains is proportional to the volume, then \(\displaystyle \alpha(V)= k V\) for constant k and the equation is relatively easy to solve.
\(\displaystyle \frac{dV}{dt}= \beta- \alpha(V)\).
Without knowing more about how the rate at which the tank drains "depends on the volume", we cannot say more. If the rate at which the tank drains is proportional to the volume, then \(\displaystyle \alpha(V)= k V\) for constant k and the equation is relatively easy to solve.
Last edited by a moderator:
D
Deleted member 4993
Guest
Generally, the outflow rate is
proportional to the height of the fluid column, and
Volume is proportional to the height of the fluid column
proportional to the height of the fluid column, and
Volume is proportional to the height of the fluid column