12 Physics Chapter 2. Mechanical properties of fluids Page 1.

This is absolute pressure at a depth d below the surface of the liquid.

Pressure increases with depth and decreases with height

Gauge Pressure

Hydrostatic Paradox:

Applications of Pascal’s Law:  

Pascal's law of fluid pressure

i) Mercury Barometer:

ii) Open tube manometer:

An open tube manometer is a simple device to measure the pressure difference.

It consists of  U-Tube partially filled with a low density  liquid (water or kerosene), 

which helps in maintaining a larger level difference between the level of liquid of the two arm of the manometer .

One arm of the tube is open to the atmosphere and other arm is connected to the container D . The system. Whose pressure is to be measured .

Consider a point R on the surface of the liquid open to the atmospheric pressure P0

consider a point T  which is exposed to the pressure of the gas in the container and another point S in the open arm of the manometer which is at the same level as point T 

The pressure at point S is given as is atmospheric pressure P0 because this arm is open to

atmosphere. 

PS = Po + hρg .........(1)

The pressure at the points S and T is the same,

Ps = PT .............(2)

The pressure at point T is,

PT = Po + hρg.........(3)

where, ρ- is the density of the liquid in the manometer, 

h- is the height of the liquid column above point S, and 

g- is the acceleration due to gravity.

According to Pascal’s principle,

pressure at T  is the same as at D, i.e., inside the chamber.

P = PT........(4)

Using Eq. (3) and Eq. (4) we can write,

P = Po + hρg.........(3)

As the manometer measures the gauge pressure of the gas in the container D, we can

write the gauge pressure in the container D as

P - P0= hρg.

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