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In fig.a below, water is to flow out from the yellow tank. But the flow is stopped because of the mercury in the green manometer. So the water is stationary. In this situation, the pressure at both the points A and B will be the same, which is ${\rho gh}$. Where ${\rho}$ is the density of water. enter image description here In fig.b, the mercury is removed from the manometer. So water flows out. In this situation, pressure at A is not equal to pressure at B. Even though A and B are at the same level. Can we give a simple explanation for such a pressure difference? I saw the basics of Bernoulli’s equation. But it does not give the reason. Thanks.

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  • $\begingroup$ A pressure difference is required for a flow to exist. $\endgroup$ Commented Oct 14, 2020 at 13:27
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    $\begingroup$ What happens when the mercury is removed from the manometer tube? The resisting pressure that was stopping the water from flowing through that tube is now gone. So now there is a pressure difference between point B and the manometer tube, which causes water to flow through the manometer tube. Once the flow begins, pressure at A and B change from their initial values; pressure at B will lie between that at A and the manometer tube. $\endgroup$
    – Deep
    Commented Oct 15, 2020 at 3:03

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The Bernoulli equation (which ignores the effect of friction) expresses conservation of energy density. Changes in pressure are included to account for the work done by pressure between the two points under consideration. If the cross section decreases, the velocity must increase. The pressure does work in increasing the kinetic energy (and can exert less force on water moving away). (By the way, the decreased pressure on the right side of the U-tube will not support a water column of the same height when the water is flowing.)

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  • $\begingroup$ I agree this is the correct explanation. I have one more doubt. In fig.b, if the area of the pipes are same at A and B, the velocities at A and B will be the same. Because, from equation of continuity, A1v1 = A2v2. Then in the Bernoulli equation, the kinetic energy quantity and potential energy quantity will be same at A and B. So the pressure energy quantity must also be same at A and B. In such a situation, there will not be any difference in pressure energies between A and B. Then how does the flow take place? $\endgroup$ Commented Oct 14, 2020 at 17:50
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    $\begingroup$ There will be a pressure difference between points (A and B) and the point where the water emerges beyond the valve. $\endgroup$
    – R.W. Bird
    Commented Oct 15, 2020 at 19:58

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