## HOW TO USE U-TUBE MANOMETER TUTORIALS

For higher pressures we can use a higher density liquid in the tube. Clearly the choice of liquids must be such that the liquid in the tube does not mix with the liquid in the pipe.

Mercury is the most commonly used liquid for the manometer tube because it has a high density (relative density of 13.6, i.e. mercury is 13.6 times denser than water) and it does not mix with common liquids since it is a metal.

To prevent it escaping from the manometer tube a U-bend is used. Note that in the diagram the height of the mercury column is labelled as x and not as h.

This is because the head is always quoted as the height of a column of the working liquid (the one in the pipe), rather than the measuring liquid (the one in the manometer tube). We therefore need to convert from x to obtain the head of working liquid that would be obtained if we could build a simple manometer tube tall enough.

To solve any conversion problem with manometers it is usually best to work from the lowest level where the two liquids meet, in this case along the level AA#.

Pressure at A is due to the left-hand column so
pA = #mgx

Pressure at A# is partly due to the right-hand column and partly due to the pressure in the pipe, so
pA# = #wlgH + pwl

We can interpret the pressure in the pipe as a pressure head using pwl = #wlghwl.

Now we know that the pressure in a liquid is constant at a constant depth, so the pressure at A must equal the pressure at A# just inside the mercury.

Therefore #mgx = #wlgH + #wlghwl To simplify this and find the pressure head:

hwl = (#m/#wl)x – H metres of the working