An open-tube manometer has one tube twice the diameter of the other. Explain how this would affect the operation of the manometer. Does it matter which end is connected to the chamber whose pressure is to be measured?

In manometer, the difference in the height of the liquid in the left and right arm of the U-tube gives the corresponding pressure.
Now, consider the diameter of the right arm is twice the left arm and left arm of the U-tube. If both the open surface is left to the atmosphere, the level of the liquid in both the arms is the same. It is due to the fact that the pressure depends on the height of the liquid column.
It is shown below:

If the left arm of the U-tube is connected to same gas, the height of the liquid column in both the arms will be different. In this case, the pressure exerted by gas is not the same with the atmosphere pressure. This is shown by the difference in their height in the tubes: