Why does closing the left arm of the U-tube doesn't change the pressure?

Question

The gif below is the exact experiment I did.

I blowed some air in the left arm and When the liquid in the right arm reached the maximum, the right arm is closed.

Keeping the right closed , I closed the left end too and then opened the right end.
When the left end was open , it was under atmospheric pressure which is defined as the weight of air column. Since I covered the left end , the weight of air column should decrease and thus the pressure should decrease and liquid should come back from the right arm to the left arm. But it doesn't happen.
I just want to know How is this possible?

Dr jh · Answer

The air in the left was at atmospheric pressure when the lid was removed. When you close the opening on the left there is no reason why the pressure should drop below atmospheric pressure.
Please note that due to gravity pushing down on the liquid on the right, this will slightly compress the air in the left, meaning it is slightly above atmospheric pressure and that is why the level of the fluid inside the left part of the tube stays the same.
You can calculate this pressure difference using Bernoulli’s equation
$$p_L + rho g h_L = p_R + rho g h_R$$
where $L$ and $R$ stand for left and right. If the pressure on the left was initially at $1  atm$ then
$$p_L = 1 + rho g (h_R - h_L)$$

Why does closing the left arm of the U-tube doesn't change the pressure?

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