Which of the following statement (s) is /are correct ?

Options

A. The equation of continuity expresses the principle of conservation of mass in fluid mechanics .
B. The Bernoull's equation express the work - energy theorem in fluid mechanics .
C. The change in plane of motion of a spring ball can be explained with the help of Bernoulli's equation .
D. The Bernoulli's equation and quation of continuity are valid for incomressible and non - viscous fluids i.e ideal fluids .

Answer

To determine which of the statements regarding fluid mechanics are correct, we will analyze each statement one by one.

### Step-by-Step Solution

1. **Statement 1: The equation of continuity expresses the principle of conservation of mass in fluid mechanics.**
- The equation of continuity states that for an incompressible fluid flowing through a pipe, the mass flow rate must remain constant from one cross-section of the pipe to another. This is derived from the principle of conservation of mass, which states that mass cannot be created or destroyed. Therefore, this statement is **correct**.

2. **Statement 2: The Bernoulli equation expresses the work-energy theorem in fluid mechanics.**
- The Bernoulli equation relates the pressure, kinetic energy, and gravitational potential energy in a flowing fluid. It shows that the total mechanical energy of the fluid remains constant along a streamline, which is a direct application of the work-energy theorem. Thus, this statement is also **correct**.

3. **Statement 3: The change in the plane of motion of a swing ball can be explained with the help of the Bernoulli equation.**
- When a fast bowler delivers a swing ball, one side of the ball is polished while the other side is rough. This difference in surface conditions causes a difference in air velocity and pressure on either side of the ball, leading to a net force that changes the direction of the ball's motion. This phenomenon can indeed be explained using the Bernoulli equation, making this statement **correct**.

4. **Statement 4: The Bernoulli equation and the equation of continuity are valid for incompressible and non-viscous fluid, i.e., ideal fluid.**
- The Bernoulli equation and the equation of continuity are both derived under the assumption of incompressible and non-viscous flow. Incompressible means that the fluid density remains constant, and non-viscous means that there are no internal frictional forces acting within the fluid. Therefore, this statement is also **correct**.

### Conclusion
All four statements are correct.