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

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To determine the time taken to empty a tank filled with water up to 20m, a differential equation is established based on the flow rate of water at 2h kg/s. The equation incorporates the density of water, the cross-sectional area of the tank, and a constant for dimensional adjustment. Initially, the height of the water column is 40m. Solving the differential equation will yield the time required to fully drain the tank. The discussion emphasizes the importance of accurately modeling the flow dynamics to achieve the correct solution.
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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Thread 'Does this series converge uniformly?'

First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...
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