The total head of a liquid particle in motion is the sum of 

Explanation:

Total Head of a Liquid Particle in Motion

The total head of a liquid particle in motion is the sum of its potential head, kinetic head, and pressure head. This is a fundamental concept in fluid mechanics, derived from the Bernoulli equation, which states that the total mechanical energy of a fluid particle remains constant along its streamline in an ideal, incompressible, and non-viscous fluid flow.

• Potential Head: This is the head due to the elevation of the particle, calculated as \( \frac{z}{g} \), where \( z \) is the elevation and \( g \) is the acceleration due to gravity.

• Kinetic Head: This is the head due to the velocity of the particle, expressed as \( \frac{v^2}{2g} \), where \( v \) is the velocity of the fluid.

• Pressure Head: This is the head due to the pressure exerted by the fluid, calculated as \( \frac{P}{\gamma} \), where \( P \) is the pressure and \( \gamma \) is the specific weight of the fluid.

Analyzing the Given Options

1. Potential head and kinetic head: (Incorrect)

   • This combination excludes the pressure head, which is a necessary component of the total head.

2. Kinetic head and pressure head: (Incorrect)

   • This combination excludes the potential head, which accounts for the elevation of the particle.

3. Potential head and pressure head: (Incorrect)

   • This combination excludes the kinetic head, which is crucial to account for the velocity of the fluid.

4. Potential head, kinetic head, and pressure head: (Correct)

   • This combination includes all three components of the total head, making it the correct answer based on the Bernoulli equation.

   • The total head is expressed as \( H = \frac{z}{g} + \frac{v^2}{2g} + \frac{P}{\gamma} \), which represents the conservation of energy in fluid motion.