Leaky Tank Differential Eqn Problem

[LongApple]

Homework Statement

http://ocw.mit.edu/courses/electric...s-fall-2011/assignments/MIT6_003F11_sol01.pdf

http://i.imgur.com/8qj5cWE.png

#6 Part B

Homework Equations

None[/B]

The Attempt at a Solution

Don't understand why we care about when r1=r0

The tank will overflow when the height of the tank is greater than 1. Why care about r1=r0? What is our motivation for think about the r1=r0 case? That's steady state sure. But they are asking about overflow which I thought just depends on water level

 

[NascentOxygen]

Once r1=r0 the water level in the top tank will cease to rise farther. If that tank has not overflowed by the stage r1 attains r0, then that tank is never going to overflow.

Each tank has two outlets: the normal outlet at its base, and the overflow being its top rim.

 

[rude man]

Don't understand why we care about when r1=r0

The tank will overflow when the height of the tank is greater than 1. Why care about r1=r0? What is our motivation for think about the r1=r0 case? That's steady state sure. But they are asking about overflow which I thought just depends on water level

View attachment 84595

Max. outflow rate of tank 1 without spilling is r₁(h_1max). This obviously must be >= r₀.
If r₀ > r₁(h_1max) then tank 1 will spill since more water has to flow out of tank 1 than its hole can accommodate.

NOTE: "r₁(h_1max)" means "r₁ of h_1max, not r₁ times h_1max.