A hydraulic turbine is a rotary machine that converts the energy of flowing or falling water into mechanical energy. The mechanical energy produced by the turbine shaft can subsequently be converted into electrical energy by coupling the turbine to a generator.

The energy available in water may exist in the form of pressure energy, kinetic energy, or potential energy. As water passes through the turbine, part of this hydraulic energy is transferred to the runner blades, causing the runner to rotate.

Hydraulic turbines are one of the most important energy-conversion devices used in hydroelectric power generation and water resource engineering.

The Turbines experiment demonstrates the conversion of hydraulic energy into mechanical energy and evaluates the performance of a hydraulic turbine under different operating conditions.

Everyday Intuition

The working principle of a hydraulic turbine can be observed in many practical situations.

• Water wheels driven by flowing streams.
• Hydroelectric power stations.
• Small hydroelectric plants in hilly regions.
• Irrigation canals used for power generation.

In each case, moving water transfers part of its energy to rotating blades and produces useful mechanical work.

The Turbines experiment provides a laboratory-scale demonstration of this energy conversion process.

Experimental Relevance

The objective of the Turbines experiment is to study the performance characteristics of a hydraulic turbine and determine its efficiency.

The experiment involves:

• Measuring the discharge through the turbine,
• Measuring the operating head,
• Measuring the rotational speed,
• Determining the output power,
• Calculating the input hydraulic power,
• Evaluating the overall efficiency of the turbine.

The experiment demonstrates how operating conditions influence the performance of hydraulic machinery.

Mathematical Formulation

The hydraulic power supplied to the turbine is

$$P_h=\rho gQH,$$

where

• $P_h$ = Hydraulic input power,
• $\rho$ = Density of water,
• $g$ = Acceleration due to gravity,
• $Q$ = Discharge,
• $H$ = Effective head.

The mechanical output power developed by the turbine shaft is

$$P_o=\frac{2\pi NT}{60},$$

where

• $N$ = Rotational speed of the turbine,
• $T$ = Torque developed by the turbine.

The overall efficiency of the turbine is

$$\eta=\frac{P_o}{P_h}\times100.$$

The efficiency indicates the fraction of hydraulic energy successfully converted into useful mechanical energy.

In practice,

$$\eta<100$$

because of hydraulic, mechanical, and frictional losses.

Application to the Turbine Apparatus

The experimental setup generally consists of

• Water supply system,
• Hydraulic turbine,
• Flow-measuring arrangement,
• Pressure measuring devices,
• Brake drum or dynamometer,
• Tachometer,
• Measuring tank.

Water is supplied to the turbine under a known head.

As water passes through the runner,

• Hydraulic energy is transferred to the blades,
• The runner rotates,
• Mechanical power is produced at the shaft.

The discharge and operating head determine the hydraulic input power.

The brake mechanism measures the shaft output power by determining the torque developed by the turbine.

The efficiency of the turbine is calculated by comparing the output power with the hydraulic input power.

Performance curves relating efficiency, power, and speed may be plotted to study the operating characteristics of the turbine.

Engineering Significance

Hydraulic turbines are widely used for renewable energy generation and water resource development.

Important applications include:

• Hydroelectric power plants,
• Small hydroelectric schemes,
• Pumped-storage systems,
• Irrigation projects,
• Water supply installations,
• Industrial power generation.

The Turbines experiment demonstrates the practical application of fluid mechanics and energy conversion principles and provides essential knowledge for the design and operation of hydroelectric systems.