Case Study about the Drainig a Tank

1. Case Study on Differential Equations

2.  The rate of change of volume with the rate of
change of liquid inside is considered.
 Change of the flow rate with respect to the
time and the initial height of the liquid
column is taken.

3.  liquid-propellant rockets.
◦ Propellant tanks are often drained at extremely
large flow rate.
◦ This is used to find-out the time taken to empty the
tank.

4.  Flow field considered is that of an
incompressible fluid.
 Tank was taken as a cylindrical of radius “a”
 Central axis of the tank was taken
perpendicular to earth surface.
 Draining is said to be a combined action of
gravity and the net pressure on the head.
 Rate of change of volume is taken dependent
of the height of fluid column.

6. 

7. 

8. 1. Take 3 different vessels of different &
uniform cross-sectional areas.
2. Fill the vessels with a similar liquid to a
definite height (h).
3. Measure the amount of liquid removed from
the vessel in a definite time (5 Seconds)
4. Take the volume of liquid removed from the
vessel in 1 second
5. Plot the graph of v and h.

9. 

10. 

11.  From these calculations we can conclude that;
◦ We can derivate an equation from a proportional
relationship and using a graphical method, we can
verify the equation.
◦ The rate of change of volume is directly
proportional to the rate of change of height of the
liquid column.
◦ The amount of liquid removed from a vessel is
equal to the product of the cross sectional area and
change of height.

12.  Thesis on “Surface deformations in a draining
cylindrical tank.” By Marshall, Franklin Lester
 www.efunda.com – Calculations on draining a
tank
 www.practicalphysics.edu – Methodology of
practical