FLUID STATICS IN FLUID MECHANICS

1. Introduction to Fluid Statics

Fluid statics is also called hydrostatics when the fluid is liquid (especially water). It is used in designing:

• Dams
• Reservoirs
• Hydraulic machines
• Ships and submarines
• Pressure measuring instruments

A fluid in static condition cannot resist shear stress. It only exerts normal stress (pressure).

2. Properties of Fluid at Rest

In fluid statics:

• Shear stress = zero
• Pressure acts normal to surface
• Pressure increases with depth

3. Pressure in Fluid

✔ Definition

Pressure is the force per unit area exerted by a fluid.$$P = \frac{F}{A}$$P=AF​

Where:
P = Pressure (Pa)
F = Force (N)
A = Area (m²)

✔ Types of Pressure

1. Atmospheric pressure
2. Gauge pressure
3. Absolute pressure
4. Vacuum pressure

$$P_{absolute} = P_{atmospheric} + P_{gauge}$$

4. Pascal’s Law

Statement:
Pressure applied to a confined fluid is transmitted equally in all directions.

This law is used in:

• Hydraulic press
• Hydraulic jack
• Hydraulic brake

Example:
In a hydraulic press, a small force applied on a small piston produces a large force on a large piston.

5. Hydrostatic Pressure

When fluid is at rest, pressure increases with depth due to the weight of fluid.$$P = \rho g h$$P=ρgh

Where:
ρ = Density of fluid
g = Acceleration due to gravity
h = Depth below free surface

👉 Key points:

• Pressure is same at same horizontal level.
• Pressure is independent of shape of container.

6. Pressure Head

Pressure head is the height of fluid column that produces a given pressure.$$h = \frac{P}{\rho g}$$h=ρgP​

Used in:

• Bernoulli’s equation
• Pump and turbine analysis

7. Manometers

Manometers are used to measure pressure.

✔ Types:

1. Simple manometer
   • Piezometer
   • U-tube manometer
2. Differential manometer

Applications:

• Measuring pressure in pipes
• Laboratory experiments

8. Forces on Submerged Surfaces

When a surface is submerged in fluid, pressure produces hydrostatic force.

✔ Total force:

$$F = \rho g A \bar{h}$$F=ρgAhˉ

Where:
A = Area
$\bar{h}$hˉ = Depth of centroid

Centre of Pressure

It is the point where the total force acts.$$h_{cp} = \bar{h} + \frac{I_G}{A \bar{h}}$$hcp​=hˉ+AhˉIG​​

Applications:

• Dam design
• Gate design
• Ship structure

9. Buoyancy and Floatation

✔ Buoyant Force

According to Archimedes principle:

A body immersed in fluid experiences an upward force equal to the weight of displaced fluid.$$F_B = \rho g V$$✔ Conditions of Floatation

A body floats when:$$Weight = Buoyant force$$Used in:

• Ships
• Submarines
• Hydrometers

10. Stability of Floating Bodies

✔ Metacentre

The point about which a floating body oscillates.

✔ Metacentric height (GM)

• If GM > 0 → Stable
• If GM < 0 → Unstable

Important in:

• Ship safety
• Floating structures

11. Fluid Statics in Accelerating Systems

Fluids at rest in accelerating containers form:

• Inclined free surface
• Parabolic surface in rotating tanks

Example:

• Fuel tanks
• Centrifuges

12. Applications of Fluid Statics

✔ Design of dams
✔ Hydraulic machines
✔ Pressure vessels
✔ Submarines
✔ Ship design
✔ Water supply systems
✔ Irrigation