Statement-1 : Bernoullis equation is based on energy conservation.
Statement-2 : Bernoullis equation can only be applied if the flow is streamlined.
Statement-3 : Bernoullies equation can be applied evern if the flow is not streamlined as total energy is always conserved.

Options

A. a.T T T
B. b.T F T
C. c.T T F
D. d.F F F

Answer

To analyze the statements regarding Bernoulli's equation, let's break them down step by step.

### Step 1: Understanding Bernoulli's Equation
Bernoulli's equation is given by:
\[ P + \frac{1}{2} \rho V^2 + \rho g h = \text{constant} \]
This equation represents the principle of conservation of energy in fluid flow, where:
- \(P\) is the pressure energy,
- \(\frac{1}{2} \rho V^2\) is the kinetic energy per unit volume,
- \(\rho g h\) is the potential energy per unit volume.

### Step 2: Evaluating Statement 1
**Statement 1:** "Bernoulli's equation is based on energy conservation."
- **Analysis:** This statement is true because Bernoulli's equation indeed arises from the conservation of mechanical energy in a fluid flow. The total energy (pressure energy + kinetic energy + potential energy) remains constant along a streamline.
- **Conclusion:** Statement 1 is **correct**.

### Step 3: Evaluating Statement 2
**Statement 2:** "Bernoulli's equation can only be applied if the flow is streamlined."
- **Analysis:** For Bernoulli's equation to hold, the flow must be steady, incompressible, and along a streamline. While it is true that Bernoulli's equation is primarily applied to streamline flow, it can also be applied in certain cases of turbulent flow under specific conditions. However, the statement implies a strict condition that is not entirely accurate.
- **Conclusion:** Statement 2 is **partially correct** but misleading as it suggests an absolute condition.

### Step 4: Evaluating Statement 3
**Statement 3:** "Bernoulli's equation can be applied even if the flow is not streamlined as total energy is always conserved."
- **Analysis:** This statement is incorrect. Bernoulli's equation is specifically applicable to streamline flow. In turbulent flow, the assumptions made in deriving Bernoulli's equation (steady flow, incompressibility, and flow along a streamline) may not hold, and thus the equation cannot be applied.
- **Conclusion:** Statement 3 is **incorrect**.

### Final Conclusion
Based on the evaluations:
- Statement 1 is correct.
- Statement 2 is misleading but has some truth.
- Statement 3 is incorrect.

Thus, the overall conclusion is that the correct option is that only Statement 1 is fully correct.