Fluid Statics

ANNEXURE

FLUID STATICS

Introduction:

The study of fluids at rest is called fluid statics. In fluids at rest, there will not be any relative motion between the adjacent layer. Under this condition the velocity gradient (du/dy) is zero which in-turn results in zero shear stress. Moreover the viscosity has no effect on fluid at rest. At rest condition the behaviour of both ideal and real fluid will be similar. In the absence of relative motion between the adjacent layers only gravity and static pressure forces need, to be considered.

1. Fluid Statics is Used to Determine the Forces Acting on the Following Application

✓ Water dams

✓ Liquid storage tanks

✓ Floating or submerged bodies

✓ Hydraulic jacks & presses

2. Fluid Pressure

It is defined as a force exerted by a fluid per unit area. It is denoted by P. It is also known as intensity of pressure.

Pressure, P = Force (F) / Area (A)

The SI unit of pressure is N/m2 (or) pascal

1 N/m2 = 1 Pa

1 KN/m2 = 1 KPa = 1 × 103 N/m2

1 MN/m2 = 1 MPa = 1 × 106 N/m2

1 bar = 1 × 105 Pa

1 Kgf/cm2 = 98.1 N/cm2 = 9.81 × 104 N/m2 or Pa

3. Pressure Head

The pressure expressed in terms of height of liquid column is known as pressure head.

Consider a vessel containing liquid as shown in fig 1.13. The liquid will exert pressure on all sides as well as bottom of the vessel, due to its own weight. When a open tube is inserted in the vessel, the liquid will rise inside the tube, The liquid filled in the open tube is called liquid column. The level of water filled in the open tube is equal to the height of liquid in the vessel.

The weight of liquid contained in the tube = mass of liquid (m) × acceleration due to gravity (g)

⇒ m × g ⇒ ρVg ⇒ ρAhg

⸪ Mass = Density (ρ) × Volume (V)

⸫ Volume = Area (A) × Height (h)

Intensity of pressure at the base of tube

The above eq is known as hydrostatic equation

Where

Specific weight of liquid, W = ρg

Density of liquid, ρ

Cross sectional area of tube, A

The indensity of pressure at any point in a liquid is directly proportional to the depth of the point measured from free surface of liquid.

P α h

P = wh (w - constant)

Pressure head h = P/w in meter of liquid.

4. Laws of Pressure

1. The intensity of pressure depends only upon the vertical height or depth of the liquid from the free surface and not up on the size and shape of the vessel.

2. The top surface of a liquid at rest will be always horizontal.

3. Intensity of pressure at any point in a liquid is same in all directions.

4. Pressure on a surface submerged in a liquid acts normal to the surface.

5. The surface of a liquid which is in contact with the atmosphere is called free surface. This surface is subjected to atmospheric pressure.

5. Atmospheric Pressure

The mass of air surrounding the earth is called as atmosphere. The atmospheric air exerts a normal pressure upon all surfaces with which the atmosphere comes in contact. This normal pressure is called atmospheric pressure.

1. Measuring Atmospheric Pressure

The standard instrument used to measure the atmospheric pressure is called barometer so the atmospheric pressure is also called barometric pressure. A tube which is sealed at one end is immersed in to a container of mercury.

The atmospheric pressure then forces mercury up into the tube higher than the mercury in the container.

Patm = ρgh

The length and cross sectional area of the tube have no effect on the height of the fluid column of a barometer.

The standard atmospheric pressure provides the force necessary to push the mercury up (in mercury barometer) the evacuated tube is 760 mm, and to push the water up (in water barometer) the evacuated is 10.33 m.

For mercury barometer

Patm = ρgh

ρ = 13600 kg/m3

g = 9.81 m/s2

h = 760 mm = 0.76 m

⸫ Patm = 101396.16 N/m2 = 101.39 Kpa

= 1.013 bar

For water barometer

Patm = ρgh

ρ = 1000 Kg/m3

g = 9.81 m/s2

h = 10.33 m

⸫ Patm = 101337 N/m2 = 101.33 KPa = 1.013 bar

In practice, water barometer is not used due to its large size and also its higher vapour pressure compared to mercury. So generally mercury barometer is used.

6. Gauge Pressure

The pressure which is measured above the atmospheric pressure is called gauge pressure. Pressure measuring instruments provide gauge pressure.

7. Vacuum Pressure

The pressure which is measured below the atmospheric pressure, is called vacuum gauge pressure. The pressure in such system is above the absolute vacuum pressure (zero pressure) but it is less than atmospheric pressure.

8. Absolute Pressure

The pressure, which is measured with respect to absolute vacuum pressure or zero pressure, is called absolute pressure.