Short Answer:

Velocity triangles help in analyzing fluid flow by showing the direction and magnitude of different velocities involved in the motion of a fluid through turbines, pumps, and other rotating machines. These triangles represent absolute velocity, relative velocity, and blade velocity using simple vectors.

By using velocity triangles, engineers can easily understand how the fluid interacts with the blades, how much energy is transferred, and what forces act on the machine. This analysis helps in calculating efficiency, power output, and designing the blades for smooth and effective fluid flow.

Detailed Explanation:

Velocity Triangles in Analyzing Fluid Flow

Velocity triangles are important tools used in fluid mechanics and hydraulic machinery to understand and calculate the behavior of moving fluid within rotating machines like turbines, compressors, and pumps. These triangles graphically represent the relationship between three types of velocities:

• Absolute velocity (V): the velocity of fluid with respect to a fixed point.
• Relative velocity (Vr): the velocity of fluid with respect to the moving blade.
• Blade velocity (U): the velocity of the rotating blade itself.

By forming a triangle using these three vectors, engineers can determine the angle at which the fluid enters and exits the blades, and how efficiently energy is transferred.

1. Understanding Fluid Motion
   Velocity triangles are drawn at both the inlet and outlet of a turbine or pump blade. They help in analyzing:

• How the fluid enters the blade (entry angle)
• How the fluid exits the blade (exit angle)
• The change in direction and speed of flow
• The energy exchanged between the fluid and the blade

These triangles help in breaking down complex fluid motion into simpler vector components, making it easier to analyze.

2. Calculation of Work and Efficiency
   Using velocity triangles, engineers can apply formulas to calculate:

• The force exerted by the fluid on the blade
• The work done by the turbine or pump
• The power output and hydraulic efficiency of the machine

By measuring the tangential component of velocity (known as whirl velocity), the torque and rotational speed can also be calculated.

3. Blade Design and Flow Optimization
   Designers use velocity triangles to create blade shapes and angles that match the direction of fluid flow.

• If the blade angle is not matched with fluid direction, energy loss occurs.
• Proper alignment ensures smooth flow, less turbulence, and better performance.

The triangles also help detect shock losses, flow separation, and cavitation risks, which can reduce machine life and efficiency.

4. Helps in Comparing Different Machines
   By using velocity triangles, engineers can compare the performance of different types of turbines (e.g., Pelton, Francis, Kaplan) or pumps.

• Each machine has its own triangle shape and flow pattern.
• These diagrams provide a standardized way to study fluid dynamics in rotating machines.

Conclusion

Velocity triangles help in analyzing fluid flow by showing how fluid enters and exits rotating blades, and how much energy is transferred. They make it easy to calculate work, efficiency, and blade angles. This method is essential in the design, operation, and optimization of turbines, pumps, and other fluid machines in civil and mechanical engineering.