Bernoulli's equation is a consequence of conservation of

Options

A. Charge
B. Mass
C. Energy
D. Temperature

Answer

To solve the question regarding Bernoulli's equation, we need to understand the fundamental principle it is based on. Here’s a step-by-step solution:

### Step 1: Understand Bernoulli's Equation
Bernoulli's equation relates the pressure, velocity, and height of a fluid in a streamline flow. It can be expressed as:
\[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \]
where:
- \( P \) = pressure energy per unit volume,
- \( \rho \) = density of the fluid,
- \( v \) = velocity of the fluid,
- \( g \) = acceleration due to gravity,
- \( h \) = height above a reference level.

### Step 2: Identify the Conservation Principle
Bernoulli's equation is derived from the principle of conservation of energy. In a flowing fluid, the total mechanical energy (sum of potential energy, kinetic energy, and pressure energy) remains constant along a streamline, provided there are no friction losses.

### Step 3: Analyze the Energy Components
In the context of Bernoulli's equation:
- The term \( P \) represents the pressure energy,
- The term \( \frac{1}{2} \rho v^2 \) represents the kinetic energy per unit volume,
- The term \( \rho gh \) represents the potential energy per unit volume due to height.

### Step 4: Conclude the Conservation Law
Since Bernoulli's equation expresses the balance of these energy forms, it is a consequence of the conservation of mechanical energy in fluid dynamics. Therefore, we conclude that:

**Bernoulli's equation is a consequence of the conservation of energy.**