What are velocity head and pressure head?

Answer

To understand the concepts of velocity head and pressure head, we will break down the explanation step by step.

### 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 remains constant. This total energy consists of three components: pressure energy, kinetic energy, and potential energy.

### Step 2: The Bernoulli Equation
The mathematical representation of Bernoulli's theorem can be expressed as:
\[ P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant} \]
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 (potential energy per unit volume)

### Step 3: Dividing the Bernoulli Equation
To express the terms in a more useful form, we can divide the entire equation by \( \rho g \):
\[ \frac{P}{\rho g} + \frac{v^2}{2g} + h = \text{constant} \]

### Step 4: Identifying Velocity Head and Pressure Head
From the modified Bernoulli equation:
- The term \( \frac{P}{\rho g} \) represents the **pressure head**. It indicates the height of a fluid column that would produce the same pressure at that point.
- The term \( \frac{v^2}{2g} \) represents the **velocity head**. It indicates the height equivalent of the kinetic energy of the fluid due to its velocity.

### Step 5: Summary of Definitions
- **Velocity Head**: \( \frac{v^2}{2g} \) (the height equivalent of the kinetic energy of the fluid)
- **Pressure Head**: \( \frac{P}{\rho g} \) (the height equivalent of the pressure energy of the fluid)