Short Answer:

The head of a turbine is the height of water or fluid available to produce energy. It represents the potential energy of the fluid due to its elevation or pressure. The higher the head, the greater the energy available to drive the turbine.

The discharge of a turbine is the volume of water or fluid flowing through the turbine per unit time, usually measured in cubic meters per second (m³/s). It represents the rate at which fluid passes through the turbine to produce power. Both head and discharge together determine the power output and efficiency of the turbine.

Detailed Explanation :

Head and Discharge of a Turbine

In hydraulic turbines, head and discharge are two essential parameters that determine the amount of energy the turbine can produce. They describe the energy available from the fluid and the quantity of fluid flowing through the system. Understanding these terms is important because they directly affect the performance, efficiency, and type of turbine used in a particular situation.

1. Head of a Turbine:
   The headof a turbine is the height or energy level difference between the water source and the outlet where the water is discharged. It indicates the potential energy available for conversion into mechanical energy. The head can be expressed in meters or feet of water column and is directly related to the pressure and velocity of the fluid entering the turbine.

There are mainly three types of head considered in turbine analysis:

• a) Gross Head:
  It is the total height difference between the water surface at the reservoir (head race) and the tail race (where water leaves the turbine). It represents the maximum potential energy available before any losses occur.
• b) Net Head:
  The net head is the actual head available at the turbine inlet after accounting for losses due to friction in the penstock and other components. It is given by:
  Net Head = Gross Head – Head Losses
  This net head is the true measure of the energy available to drive the turbine blades.
• c) Effective Head:
  Sometimes, the term “effective head” is used to represent the head that truly acts on the runner to produce work. It includes minor corrections for velocity and pressure effects at the turbine entrance.

The head plays a very important role in determining the type of turbine used.

• For high head (above 250 m), Pelton wheel turbines are used.
• For medium head (30–250 m), Francis turbines are suitable.
• For low head (below 30 m), Kaplan or propeller turbines are preferred.

Hence, the head not only defines the available energy but also guides the selection and design of the turbine.

2. Discharge of a Turbine:
   The dischargeof a turbine refers to the volume of fluid (generally water) passing through the turbine per unit time. It is denoted by the symbol Qand measured in cubic meters per second (m³/s) or liters per second (L/s). It represents the quantity of fluid available for energy conversion.

Mathematically,
Discharge (Q) = Area of Flow × Velocity of Flow

The discharge determines how much kinetic energy is carried by the fluid into the turbine. If the discharge is large, more energy can be transferred to the turbine blades, resulting in higher power output. However, the discharge also depends on the type of turbine and the head available. For example, high-head turbines like the Pelton wheel have low discharge, whereas low-head turbines like Kaplan or Francis have high discharge.

Proper control of discharge is necessary for maintaining turbine efficiency and protecting it from overloading. Flow control devices such as governor valves, guide vanes, or nozzles are used to adjust discharge as per the load demand.

3. Relationship Between Head, Discharge, and Power:
   The power developed by a turbine depends on both head and discharge. The basic formula for hydraulic power is:

Power = ρ × g × Q × H × η

Where,
ρ = Density of water (kg/m³)
g = Acceleration due to gravity (9.81 m/s²)
Q = Discharge (m³/s)
H = Net Head (m)
η = Efficiency of the turbine

From this formula, it is clear that increasing either head (H) or discharge (Q) will result in higher power output, provided the turbine efficiency remains constant. Engineers use these parameters to design turbines suitable for specific conditions of water flow and height.

4. Importance of Head and Discharge:

• The head determines the velocity and energy of the water entering the turbine.
• The discharge controls the amount of water available to produce energy.
• The combination of both helps in selecting the right type of turbine and predicting the amount of electricity generated.
• Monitoring both parameters ensures safe operation, prevents overloading, and maintains consistent performance.

Conclusion:

In conclusion, the head and discharge of a turbine are two vital factors that define its working capacity and efficiency. The head represents the energy available due to the height or pressure of water, while the discharge indicates the quantity of water flowing through the turbine. Together, they determine the total hydraulic power that can be converted into mechanical and electrical energy. Proper measurement and control of these parameters are essential for efficient turbine design, operation, and performance in hydroelectric power systems.