Hydrostatic Problem: Three tube Manometer

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Mokha75
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Hi guys, new to the forum here.

I have of a conceptual question that I can't wrap my head around.

Here's the situation: there's a reservoir filled with water attached to a "three-column manometer" with each column open to the atmosphere. The horizontal tube that connects all three of the columns at the bottom, has a valve at the end. The valve is in the closed position and then opened to let the water run through.

What I would like to know is when we do this, for a given time period, why do see the water in the column closest to the valve (column 3 below) have a greater change in height as compared to the column closest to the reservoir (column 1)?

Hope I'm making sense

here's my lame attempt at drawing the apparatus:

(__Reservoir__)-------I--------------I-------------I--valve
Column 1 Column 2 Column 3
 
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Well, the flow of matter from one side to another will occur due to a pressure difference between the reservoir and valve. The water in the horizontal tube experiences a pressure gradient from the reservoir to the valve, and that is what causes the flow in that direction.

At the same time, this pressure gradient can be observed by placing several vertical columns along the horizontal tube.