Short Answer:

Velocity diagrams in hydraulic turbines are used to show how water flows through the turbine blades and how its velocity changes during energy conversion. These diagrams help understand the direction and magnitude of water velocity at different points, such as the inlet and outlet of the runner.

By analyzing velocity diagrams, engineers can calculate important values like work done, blade angles, and efficiency. They are especially useful in designing and improving the performance of turbines like Pelton, Francis, and Kaplan.

Detailed Explanation:

Role of velocity diagrams in hydraulic turbines

Velocity diagrams are graphical tools that help visualize and analyze the flow of water through turbine blades in hydraulic turbines. These diagrams represent the relative, absolute, and blade velocities of water at different points in the turbine. The flow of water is not always straight, and its direction and speed can change as it moves through the turbine blades. Velocity diagrams allow engineers to understand these changes clearly and use the information to calculate power output, efficiency, and blade design.

There are usually two velocity triangles drawn for each turbine:

• Inlet velocity triangle (at the entry of water to the runner)
• Outlet velocity triangle (at the exit of water from the runner)

Each triangle is made up of:

1. Absolute velocity (V) – actual speed of water.
2. Relative velocity (Vr) – speed of water with respect to the moving blade.
3. Blade (or tangential) velocity (U) – speed of the blade at that point.

Purpose and Role in Turbine Analysis

1. Determine work done by water
   The main use of velocity diagrams is to calculate the work done on the turbine blades by water. According to Euler’s turbine equation, the work is directly related to the change in the whirl component of the absolute velocity. This is clearly visible in the velocity triangles.
2. Calculate blade angles
   For water to enter and exit the blades smoothly, the blade inlet and outlet angles must match the water flow angles. Velocity diagrams help find these angles accurately, which improves turbine performance and avoids losses due to improper entry or exit of water.
3. Find turbine efficiency
   By studying velocity diagrams, engineers can find the amount of energy extracted from water and compare it to the total energy available. This helps calculate the hydraulic efficiency of the turbine.
4. Design and optimize turbines
   Velocity diagrams help in designing the shape and orientation of the turbine blades. For example, in Francis turbines, both radial and tangential flows are considered, while Pelton wheels work purely on jet impact. Diagrams ensure the blades are designed correctly for the expected velocity profile.
5. Visualize flow direction
   These diagrams make it easy to visualize the direction of water flow relative to the moving blades. This is important for understanding how forces act on the blades and how energy is transferred from the fluid to the runner.

Application in Different Turbines

• Pelton Turbine: Uses velocity triangles to measure jet impact and runner movement.
• Francis Turbine: Mixed flow, so velocity diagrams help handle both radial and axial components.
• Kaplan Turbine: Axial flow, so diagrams are used to analyze axial velocity and blade speed.

Conclusion:

Velocity diagrams play a key role in understanding and analyzing how water flows through hydraulic turbines. They help calculate energy conversion, design blade angles, and evaluate turbine efficiency. These diagrams are an essential tool in turbine design, performance analysis, and improving overall energy output in hydroelectric projects.