How much Can Each Pump Remove in 1 Hour? Equation Solution

  • Thread starter Thread starter allenh
  • Start date Start date
  • Tags Tags
    Stuck
allenh
Messages
4
Reaction score
0
If a first pump is used for 2.2 hours and a second pump is used used for 2.7 hours,32m cube can be removed from a waste water holding tank. If the first pump is used for 1.4 hours and the second pump used for 2.5 hours,24m cube can be removed. How much can each pump remove in 1 hour ?.
What is the result to two significant digits ?
 
Physics news on Phys.org
This should be in the homework section, and it's not really a differential equation

Start by writing down the speed of each pump (in meters cubed/hour), say v1 and v2. You should be able to write down two linear equations with these variables
 
There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
Are there any good visualization tutorials, written or video, that show graphically how separation of variables works? I particularly have the time-independent Schrodinger Equation in mind. There are hundreds of demonstrations out there which essentially distill to copies of one another. However I am trying to visualize in my mind how this process looks graphically - for example plotting t on one axis and x on the other for f(x,t). I have seen other good visual representations of...
Back
Top