In Bernoulli's theorem which of the following is conserved?

Options

A. Mass
B. Energy
C. Liner momentum
D. All the above

Explanation

To solve the question regarding what is conserved in Bernoulli's theorem, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Bernoulli's Theorem**:
Bernoulli's theorem states that for an incompressible, non-viscous fluid flowing in a streamline motion, the total mechanical energy of the fluid remains constant. This total energy is the sum of the pressure energy, kinetic energy, and potential energy.

2. **Identifying the Types of Energy**:
- **Pressure Energy (P)**: This is the energy due to the pressure exerted by the fluid.
- **Kinetic Energy (KE)**: This is the energy due to the motion of the fluid, calculated as \( \frac{1}{2} mv^2 \).
- **Potential Energy (PE)**: This is the energy due to the height of the fluid in a gravitational field, calculated as \( mgh \).

3. **Formulating the Energy Conservation Equation**:
According to Bernoulli's theorem, the total energy at any two points in the flow (point 1 and point 2) can be expressed as:
\[ P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2 \]
Here, \( P \) is the pressure, \( v \) is the velocity, \( g \) is the acceleration due to gravity, and \( h \) is the height.

4. **Conclusion**:
From the above formulation, it is clear that the total energy (which includes pressure energy, kinetic energy, and potential energy) is conserved in a flowing fluid according to Bernoulli's theorem.

5. **Final Answer**:
Therefore, the correct answer to the question "In Bernoulli's theorem which of the following is conserved?" is **Option 2: Energy**.