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

The gif below is the exact experiment I did.

I blew some air into the left arm and when the liquid in the right arm reached the maximum, the right arm was 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 the air column. Since I covered the left end, the weight of the air column should decrease and thus the pressure should decrease and liquid should come back from the right arm to the left arm. But that doesn't happen.

I just want to know how is this possible?

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

$$p_L = 1 + \rho g (h_R - h_L)$$

• so closing the left end doesn't decrease that atmospheric pressure ? It is the weight of air column , so doesn't the weight change when the amount of air is decreased ? Nov 23, 2020 at 8:13
• why should we consider the effect of gravity after closing the left arm and not when it was open ? Gravity pulls the right end and the excess pressure in the left end should be transferred when it was open ... Nov 23, 2020 at 8:18
• We are considering gravity ALWAYS. You need to look at Bernoulli’s equation which contain $g$. When it’s closed do you not believe that gravity will cause the gas in the left to slightly compress? Nov 23, 2020 at 8:24