In the previous article, we learned about the physical properties of fluids. In this article, we will learn about the concept of pressure measurement, which is an important topic to understand for the sake of scroing good marks in GATE, UPSC and other exams in Mechanical Engineering. 

The device we must know about fluid pressure measurement is manometer. It is a device that measures the fluid pressure by the height of a liquid column. Take for example, the case of measuring the pressure of liquid flowing inside a pipe, the presssure p can be determined by measuring the height of liquid coming upwards into a manometer which is positioned in an upright manner, check figure(a) below.

 

 If  is the atmospheric pressure and  is the density, the following equation is obtained:

When the pressure becomes large, the above equation becomes inconvinient to use as becomes too high. So that calls for the use of U-tube manometer, as shown in figure(b) above, which contains a high density liquid like mercury. Let us assume that the density in this case is , then

or

In the case of measuring the pressure difference between two pipes in both of which a liquid of density  flows, a differential manometer as shown in the figure below is used. 

In the figure(a) above, the differential pressure of the liquid is small and the measurements are done by filling the upper section of the meter with a liquid whose density is less than that of the liquid to be measured, or with a gas. So,

and in the case, where density  is of a gas,

Figure (b) of a differential manometer is used when the differential pressure is large. In this case, a liquid column of a larger density than the measuring fluid is used. So,

and in the case, where density  is of a gas,

A U-tube manometer shown in figure above becomes inconvenient for measuring fluctuating pressure, because in order to measure the difference in pressure, it is necessary to read both right and left water levels simultaneously. In case of fluctuating pressure, if the sectional area of one of the tubes is made large enough, as shown in the figure below, the water column of height H could be measured by just reading the liquid surface level in the other tube as the surface fluctuation of liquid in the tank can be ignored.

In order to measure a very minute value of pressure, a glass tube is inclined at an appropriate angle as shown in the figure below, which is called an inclined manometer. When the angle of inclination is  and the movement of the liquid surface level is L, the differential pressure H is as shown in the equation, .

According to this, if  is made smaller, the reading of the pressure is magnified. 

Now, let us look at an example of pressure calculation by manometers.

Example: A manometer is fitted as shown in the figure below. Determine the pressure at point A. 

 

Sol:

With respect to datum at B, pressure at left hand side = pressure at right hand side.

 considering the left limb

 

Considering the right limb, 

  expressred as gauge pressure

  =   gauge