STATEMENT - 1 Bernoulli's theorem is conversation of energy
because
STATEMENT - 2 Mass flowing per second at every cross section in tube of flow corresponding to incompressible liquid remains constant.

Options

A. Statement - 1 is True , Statement - 2 is True , Statement - 2 is a correct explanation for Statement - 2
B. Statement -1 is True , Statement - 2 is True , Statement - 2 is Not a correct explanation for Statement - 1 .
C. Statement - 1 is True , Statement - 2 is False
D. Statement - 1 is False , Statement - 2 is True

Answer

To solve the question, we need to analyze both statements provided and determine their validity and relationship.

### Step 1: Understanding Bernoulli's Theorem
Bernoulli's theorem states that for an incompressible, non-viscous fluid flowing in a streamline, the total mechanical energy along a streamline is constant. This total energy comprises three components:
1. Kinetic Energy per unit volume: \( \frac{1}{2} \rho v^2 \)
2. Potential Energy per unit volume due to height: \( \rho g h \)
3. Pressure Energy per unit volume: \( P \)

The Bernoulli equation can be expressed as:
\[ \frac{1}{2} \rho v^2 + \rho g h + P = \text{constant} \]
This indicates that the sum of these energies remains constant for any point along the streamline, thus confirming that Bernoulli's theorem is indeed a statement of conservation of energy.

### Step 2: Understanding the Continuity Equation
The continuity equation states that for an incompressible fluid, the mass flow rate must remain constant from one cross-section of a tube to another. Mathematically, this can be expressed as:
\[ A_1 v_1 = A_2 v_2 \]
where \( A \) is the cross-sectional area and \( v \) is the fluid velocity at different sections. This means that the product of the cross-sectional area and the fluid velocity at any two points in the flow must be equal, ensuring that mass is conserved.

### Step 3: Evaluating the Statements
- **Statement 1**: "Bernoulli's theorem is conservation of energy."
- This statement is **true** as it correctly describes the principle behind Bernoulli's theorem.

- **Statement 2**: "Mass flowing per second at every cross-section in a tube of flow corresponding to incompressible liquid remains constant."
- This statement is also **true** as it accurately describes the continuity equation.

### Step 4: Relationship Between the Statements
While both statements are true, they describe different principles:
- Statement 1 pertains to conservation of energy (Bernoulli's theorem).
- Statement 2 pertains to conservation of mass (continuity equation).

Thus, Statement 2 does not serve as a correct explanation for Statement 1.

### Conclusion
The correct answer is:
- Statement 1 is true.
- Statement 2 is true.
- Statement 2 is not a correct explanation of Statement 1.

### Final Answer
Option 2: Statement 1 is true, Statement 2 is true, but Statement 2 is not a correct explanation of Statement 1.

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