Conical tank Dynamics

S

Sachin Abhane

Dynamics of the following conical tank is to
be studied.(i.e. Relation between height & time)
upper diameter = 15cm
lower diameter = 4.5 cm
height = 29 cm
There is resistance to flow at bottom .

When inflow = 90 cc/s
steady state height = 22.2 cm

when given a step change to make inflow = 95cc/s
steady state height = 25.3 cm.
Time taken =1800 seconds
Relation between height and time between the 2 steady states is to be found

J

jmGiraud

Dynamics of tank:
The solution starts knowing the dynamic of a pure liquid column. The Toricelli equation gives velocity at bottom of the column.
v=SQRT(h).
So, the height it fills in so much time will rflect this law. Taking into account velocity in the two point and the variation in the change in volume.
This law vanishes is the flow is very laminar at the tank outlet. It would then follow the Poiseuille law of laminar viscous flow.