1. What is Fluid Dynamics?

Fluid Dynamics deals with the motion of fluids considering the forces causing the motion.

It is concerned with:

Pressure forces
Gravity forces
Inertia forces
Energy of flowing fluid

While kinematics studies only motion, dynamics studies motion + forces

2. Forces Acting on a Flowing Fluid

A moving fluid is subjected to:

Force	Cause
Pressure force	Due to fluid pressure
Gravity force	Due to weight of fluid
Viscous force	Due to fluid friction
Surface tension force	Due to molecular attraction

3. Euler’s Equation of Motion

For a flowing fluid, applying Newton’s 2nd law:

\text{Force} = \text{Mass} \times \text{Acceleration}

This gives Euler’s equation along a streamline:

\frac{dp}{\rho} + g dz + V dV = 0

This is the basic equation of fluid dynamics

4. Bernoulli’s Theorem

Derived from Euler’s equation for ideal flow.

Statement

For an incompressible, frictionless fluid in steady flow, the total energy per unit weight remains constant along a streamline.

Mathematical Form

\frac{p}{\gamma} + \frac{V^2}{2g} + z = Constant

Where:

Term	Meaning	Name
$\frac{p}{\gamma}$	Pressure head	Pressure energy
$\frac{V^2}{2g}$	Velocity head	Kinetic energy
$z$	Datum head	Potential energy

This is called the Bernoulli equation

5. Assumptions of Bernoulli’s Theorem

Valid only if:

Flow is steady
Fluid is incompressible
Flow is frictionless
Flow is along a streamline
No external work is done

6. Modified Bernoulli Equation (Real Fluids)

For actual fluids, losses and machines are included:

\frac{p_1}{\gamma} + \frac{V_1^2}{2g} + z_1 + h_p = \frac{p_2}{\gamma} + \frac{V_2^2}{2g} + z_2 + h_L + h_t

Where:

$h_p$ = Head added by pump
$h_t$ = Head removed by turbine
$h_L$ = Head loss due to friction

7. Applications of Bernoulli’s Theorem

(A) Venturimeter

Measures discharge in pipes.

Discharge equation:

Q = C_d \frac{A_1 A_2}{\sqrt{A_1^2 - A_2^2}} \sqrt{2g h}

(B) Orificemeter

Also measures discharge using pressure difference.

(C) Pitot Tube

Measures velocity at a point.

V = \sqrt{2 g h}

(D) Flow over Notches and Weirs

Used in open channel flow measurement.

8. Momentum Equation

Based on Newton’s 2nd law

\text{Force} = \text{Rate of change of momentum}

F = \rho Q (V_2 - V_1)

Used for:

Force on pipe bends
Force on nozzles
Jet impact on plates and vanes

9. Impulse–Momentum Principle

Change in momentum causes force.

Example: Jet striking a plate

F = \rho Q V

10. Energy Line and Hydraulic Grade Line

Energy Grade Line (EGL)

Represents:

\frac{p}{\gamma} + \frac{V^2}{2g} + z

Hydraulic Grade Line (HGL)