How Does Water Flow Rate Change Over Time in a Draining Cylinder?

[unsung-hero]

Homework Statement

Ok, so the height of the cylinder is 5.5 meters. The radius is 1 meters.
There is a hole, .5 meters from the bottom(5 meters from the top), its radius is .02 meters.

The question is how fast does water flow out, relative to time(this because the height of the water keeps dropping, so the flow rate decreases). [/B]

Thank You :)

Homework Equations

Am i doing it right?
If i am, can you please solve it(i can't quiet figure it out)?
Please give the rate of change of the flowrate(dflowrate/dt).
Also, rate of change of height(dh/dt).
[/B]

The Attempt at a Solution

Height = total volume - (integral sign) flowrate dt
flowrate = (cross sectional area * Velocity(

) * density

dflowrate/dt = (deritive of the expression above)[/B]

 

[Chestermiller]

Suppose that h(t) is the height of the fluid level in the cylinder at time t, and R is the radius of the cylinder. What is the volume of fluid in the cylinder V(t) at time t?

Chet