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


The drawback to this approach of concentrating on liquids is that liquids are very dense compared with gases and so we do not have to go very far down into a liquid before the pressure builds up enormously due to the weight of all the mass of liquid above us. This variation of pressure with depth is almost insignificant in gases.

If you were to climb to the top of any mountain in the world, then you would not notice any difference in air pressure even though your altitude may have increased by about 1000 metres. In a liquid, however, the difference in pressure is very noticeable in just a few metres of height (or depth) difference.

Anyone who has ever tried to swim down to the bottom of a swimming pool will have noticed the pressure building up on the ears after just a couple of metres. This phenomenon is, of course, caused by gravity which makes the water at the top of the swimming pool press down on the water below, which in turn presses down even harder on the ears.

In order to quantify this increase of pressure with depth we need to look at the force balance on a submerged surface, so let us make that surface an ear drum, as shown in Figure 3.1.7

We are dealing with gravitational forces, which always act vertically, and so we only need to consider the effect of any liquid, in this case water, which is vertically above the ear drum. Water which is to either side of the vertical column drawn in the diagram will not have any effect on the pressure on the ear drum, it will only pressurize the cheek or the neck, etc.

The volume of water which is pressing down on the ear drum is the volume of a cylinder of height h,\ equal to the depth of the ear, and end area A, equal to the area of the ear drum,

Volume = hA

Therefore the mass of water involved is
Volume × density = #hA where # is the density in kg/m3 and the weight of this water is
Mass × gravity = #ghA

We are interested in the pressure p rather than this force, so that we can apply the result to any shaped surface. This pressure will be uniform across the whole of the area of the ear drum and we can therefore rewrite the force due to the water as pressure × area. Hence: pA = #ghA

Cancelling the areas we end up with:
p = #gh

Since the area of the eardrum cancelled out, this result is not specific to the situation we looked at; this equation applies to any point in any liquid. We can therefore apply this formula to calculate the pressure at a given depth in any liquid in an engineering situation.

There are two further important features that need to be stressed:

  1. Two points at the same depth in the same liquid must be at the same pressure even if one of them is not directly underneath the full depth.
  2. # The same pressure due to depth can be achieved with a variety of different shaped columns of a liquid since only the vertical depth matters   


When the fuel is well ignited, its temperature will be far above that of ignition. While combustion is taking place, if the temperature of the elements is lowered (by whatever means) below that of ignition, combustion will become imperfect or will cease, causing waste of fuel and the production of a large amount of soot.

Since it is the purpose to develop into heat all the latent energy in the fuel, it is important that the temperature of the fuel be kept as high as practical. The maximum temperature attainable will depend generally on four factors:

1. It is impossible to achieve complete combustion without an excess amount of air over the theoretical amount of air required, and the temperature tends to decrease with the increase in the amount of excess air supplied.

2. If this excess air be reduced to too low a point, incomplete com- bustion results and the full amount of heat in the fuel will not be liberated.

3. With high rates of combustion, so much heat can be generated that, in a relatively small space, even if the excess air is reduced to the lowest possible point, the temperatures reached may damage the containing vessel.

4. Contrary-wise, if the containing vessel is cooled too rapidly (by whatever means), the temperature of the burning fuel may be lowered resulting in poor efficiency.

The rate of combustion, therefore, affects the temperature of the fire, the temperature increasing as the combustion rate increases, provided that relation of fuel to air is maintained constant.

Temperatures of 3000°F may be reached at high rates of combustion and low amounts of excess air and may cause severe damage to heat resisting materials and other parts of the containing vessel.


When air is supplied to a fuel, the temperature must be high enough or ignition will not take place and burning will not be sustained. Nothing will burn until it is in a gaseous state.

For example, the wax of a candle cannot be ignited directly; the wick, heated by the flame of a match, draws up a little of the melted wax by capillary action until it can be vaporized and ignited. Fuels that liquefy on heating usually will melt at a temperature below that at which they ignite.

Solid fuels must be heated to a temperature at which the top layers will gasify before they will burn. The ignition temperatures of fuels depend on their compositions; since the greatest part is carbon, the temperature given in the table, 870°F, will not be far wrong.

Heat must be given to the fuel to raise it to the temperature of combustion. If there is moisture in the fuel, more heat must be supplied before it will ignite, since practically all of the moisture must be evaporated and driven out before the fuel will burn.

Temperature may be measured by its effect in expanding and contracting some material, and is usually measured in degrees. The mercury thermometer is a familiar instrument in which a column of mercury is enclosed in a sealed glass tube and its expansion and contraction measured on an accompanying scale.

Two such scales are in common use, the Fahrenheit (F) and the Centigrade or Celsius (C). The former has the number 32 at the freezing point of water and 212 at the boiling point; thus 180 divisions, or degrees, separate the freezing and boiling points or temperatures of water.

The latter has the number zero (0) at the freezing point of water and 100 at the boiling point; thus 100 at the boiling points thus 100 divisions or degrees separate the freezing and boiling points or temperatures of water. Both scales may be extended above the boiling points and below the freezing points of water.

Other instruments may employ other liquids, gases, or metals, registering their expansion and contraction in degrees similar to those for mercury.


Perfect combustion is the result of supplying just the right amount of oxygen to unite with all the combustible constituents of the fuel, and utilizing in the combustion all of the oxygen so supplied that neither the fuel nor the oxygen may be left over.

Complete combustion, on the other hand, results from the complete oxidation of all the combustible constituents of the fuel, without necessarily using all the oxygen that is left over. Obviously, if extra oxygen is supplied, it must be heated and will finally leave the boiler carrying away at least part of the heat, which is thereby lost.

If perfect combustion could be obtained in a boiler there would be no such waste or loss of heat. The more nearly complete combustion can approach a perfect combustion, the loss will occur in the burning of a fuel. The problems of design and operation of a boiler are contained in obtaining as nearly as possible perfect combustion.

When fuels are burned, they not only produce the combustion products indicated in the chemical equations listed above. More importantly, they also produce heat. The heat will cause the temperature of the gases and the surrounding parts to rise.

The distinction between temperature and heat must be clearly understood. Temperature defines the intensity, that is, how hot a substance is, without regard to the amount of heat that substance may contain.

For example, some of the boiling water from a kettle may be poured into a cup; the temperature of the water in the kettle and the cup may be the same, but the amount of heat in the greater volume of water in the kettle is obviously several times the amount of heat contained in the water in the cup.

If two bodies are at different temperatures, heat will tend to fl ow from the hotter one to the colder one, just as a fluid such as water tends to flow from a higher to a lower level.