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When using Bernoulli's Equation we sometimes assume that the velocity is zero if the tank is very large. Why can we do this? Is it because the pressure is assumed to be zero as well?

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    $\begingroup$ It's not zero, but insignificant. $\endgroup$ – Mast Sep 18 at 8:45
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By conservation of volume, you must have the same flow rate at the surface as the flow rate through the tube/exit. If the tank is at least 10 times the diameter then it has at least 100 times the area. That means the exit velocity is at least 100 times faster and the velocity term in the bernoulli equation is 10000 times bigger at the exit than the velocity term at the surface. Thus for "large" tanks that small term is ignored.

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For an incompressible fluid the continuity equation becomes

$$V_{1}A_{1}=V_{2}A_{2}$$

Which says the volume flow rate is constant (fluid is neither piling up or being depleted within the tank). So the larger the cross sectional area $A$, say at the top of the tank, the lower the flow velocity $V$ to maintain the same volume flow rate as at the lower cross sectional area at the tank exit. If $A_1$>>$A_2$, then $V_1$<<$V_2$ and can be neglected.

Hope this helps

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