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For the same pressure and length, flow does depend on the pipe diameter, but I would think 2.5" pipe should be more than enough for domestic needs: even if sometimes you need higher flow, your tank would help meet the greater demand for a limited time. The pipe diameter would matter if it were too small to provide the required amount of water even if the ...

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The characteristic length is the dimension that defines the length scale of a physical system. This implies that for any system, which my contain several length scales, there may only be one characteristic length scale. This is also generalizable to the other characteristic scales such as time, speed, etc. As you may have read in my other answer, generally ...

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If the formation height is constant and you use the 1D form of the equation, then x must be measured along the channel and h is a linear function of x. In particular, $$v=-K\frac{dh}{dx}$$ where v is the superficial velocity (constant) in the x direction and K is the hydraulic conductivity. If $h_2>h_1$, the flow is in the negative x direction. In the ...

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Are there any preconditions for a form and shape of the time modes (chronoi)? Yes, there are. The modes must be orthogonal, so for any $ij$ there must be $(\Psi_i,\Psi_j) = \delta_{ij}$. Hence there are in practical point of view limited options of shapes: If the first mode is "sine-like" than the second should be "cos-like", then the argument shoud be ...

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