The U tube manometer

The fact that the pressure at a certain level in a liquid is the same at all points at that level is used in the manometer – a device for measuring pressure or comparing the densities of two liquids.

In Figure 1 a U tube is partly filled with liquid. The pressure of the air on both the open ends is the same, the pressure at the points A and B must be the same (same level in the liquid) and so the levels of the top of each limb of the U tube are equal.

In Figure 2 the U tube is still partly filled with liquid but this time someone blows into the right hand open end. The pressure at the points A and B must still be the same (same level in the liquid) and so the height of the column of liquid on the right is less than that on the left.
The pressure at A is due to the ordinary air pressure plus the height of the column above A and the pressure at B is the higher air pressure plus the liquid column above B.

In Figure 3 the U tube contains two different liquids. The yellow liquid on the right has a higher density than the blue liquid on the left and so less of it is needed to give the same pressure at points A and B. The pressure at the points A and B must still be the same.
The pressure at A is due to the ordinary air pressure plus the height of the column above A and the pressure at B is the higher air pressure plus the liquid column above B.

Measurement of pressure using a manometer

If the pressure on one limb of a U tube is greater than the other this difference in pressure can be measured by simply finding the DIFFERENCE in height (h) of the liquid in the two limbs of the U tube. In the diagram shown here (Figure 4) this difference is 11 cm.

This apparatus can be used to measure the pressure of your lungs above atmospheric pressure by simply blowing into one end of a long U tube and the finding the difference in liquid levels. If water is used as the liquid in the U tube your lung pressure will be anything between about 50 and 200 cm of water. This means that you could hold up a column of water between 50 and 200 cm high just by blowing.




The actual pressure above atmospheric in pascals can be worked out using the formula:

Pressure = depth x density x gravity = 0.11 x 1000 x 10 = 110 Pa
(Acceleration due to the Earth's gravity = 10 m/s² and density of water = 1000 kg/m³)