Time to Empty a Tank with Water Flowing at 2h kg/s

Manshah
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a tank is filled with water up to its brim a hole was made at the bottom of tank find time taken to empty tank if water flows at rate of 2h kg/s where h is height of liquid column and is equal to 20m radius is equal to h/2

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Differential equation for change of mass in the tank for infinitesimal time change dt is
\rho dV=\rho Adh =-2h c dt
where ##\rho## is density of water ##1000 kg/m^3##, A is horizontal cross section area ##2*20*\pi ##m^2, c is constant to adjust physical dimension c = 1 kg /(sec meter). h=40 m when t=0.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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