Chapter 10, Problem 10.44SP

Interpretation Introduction

Interpretation:

In a mercury-filled open end manometer the level in the arm connected to the container is 17.6 cm lower than that of the level of the arm open to the atmosphere and the atmospheric pressure reading outside the apparatus is 754.3 mm Hg. Calculate the pressure inside a container in millimetres.

Concept introduction:

Pressure is force per unit area.

  $\begin{array}{c}P=\frac{F}{A}=\frac{N}{m^2}\\ =\frac{m\cdot a}{m^2}=\frac{kg\cdot \frac{m}{s^2}}{m^2}=\frac{kg}{m\cdot s^2}\end{array}$

Its unit is Newton per meter square or we can say kilogram per meter per Second Square. These two are not the only units of pressure. The International system of unit (S.I unit) of pressure is Pascal, but these are not the only units of pressure there are more units of pressure like pounds per square inch, atmospheric (atm), mm Hg, torr etc.

The pressure is measured in the U-tube as shown below: The pressure is measured by filling water into this tube so that the difference between the lengths of two sides of U-tube gives an idea about the pressure. In this tube, one end is kept at room atmospheric pressure and the other side to that whose pressure has to be measured. So, this is the reason for the different units of the pressure because the length can be measured in different units. In the case of water, there would be a requirement of a large U-tube so mercury is used instead of water because its density is more than that of water. So, another unit of pressure was invented that is mmHg.

To determine:

The pressure in millimetre in the open end manometer.