# A math or a simple fluid problem?

by hanson
Tags: fluid, math, simple
 P: 320 Hi all! I am solving for the height of a tank as a function of time. The tank has a constant inflow of a and is subjected to small fluctuation of bsin(wt). So the inflow is simply a+bsin(wt). The outflow should be proportional to the square root of the height, H. So outflow = c*sqrt(H) Therefore the below differential equation is obtained with k=the area of the tank: $$\frac{a+bsinwt-c\sqrt{H}}{k}=\frac{dH}{dt}$$ but the problem is that I don't know how to solve this ODE... Can anyone solve the problem?
 PF Patron Sci Advisor P: 1,481 Have you been given this equation or have you set it up by yourself?
 P: 320 I set it up myself. And I have show my deduction: The tank has a constant inflow of a and is subjected to small fluctuation of bsin(wt). So the inflow is simply a+bsin(wt). The outflow should be proportional to the square root of the height, H. So outflow = c*sqrt(H) Therefore the above differential appears. Am i correct?
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