Thread: differential modelling

Can someone pls help me out with this question.
As water floes out from a straight cylindrical vessel, the rate of change of the height of the free surface level is directly proportional to the square root of the height.It os observed that the height at t=o is h02.25m and at t=90s h=1.75m.When will be height be h=1.25m

Originally Posted by lakuzy100

Can someone pls help me out with this question.
As water floes out from a straight cylindrical vessel, the rate of change of the height of the free surface level is directly proportional to the square root of the height.It os observed that the height at t=o is h02.25m and at t=90s h=1.75m.When will be height be h=1.25m

The statement

the rate of change of the height of the free surface level is directly proportional to the square root of the height

tells us how to set up the differential equation.

It tells us that the rate of change of the height is directly proportional to the square root of the height

Thus, our DE is , where is some constant of proportionality.

To solve, apply the separation of variables technique:



Integrating both sides, we see that



Use the first condition to find C.

Then use the second condition to find k.

Finally, find the time it takes to reach a height of 1.25.

Can you take it from here?

--Chris