The rotor shown in Fig. P 12.1 rotates clockwise. Assume...

The rotor shown in Fig. $P 12.1$ rotates clockwise. Assume that the fluid enters in the radial direction and the relative velocity is tangent to the blades and remains constant across the entire rotor. Is the device a pump or a turbine? Explain.

Key Concepts

Blade Geometry and Flow Entry Angle

The way in which the fluid enters a rotating device and the geometry of the blades play a crucial role in determining the nature of the energy exchange. A radial entry combined with blades that cause the relative velocity to be tangent to the flow suggests that the design is intended to add energy to the fluid, a hallmark of pump operation.

Relative Velocity

Relative velocity refers to the speed and direction of the fluid as observed from the moving frame of the rotor blades. When it is tangent to the blades it signifies that the flow is oriented along the blade surfaces, which in the context of a pump means the rotor is effectively imparting energy to the fluid, directing its flow and increasing its pressure.

Pump vs. Turbine

In turbomachinery the essential difference is in the direction of energy transfer: a pump adds work to the fluid (increasing its pressure and velocity), while a turbine extracts energy from the fluid (converting the fluid’s energy into mechanical work). The classification depends on whether energy is being imparted to or taken from the fluid during the rotor–fluid interaction.

Energy Transfer in Rotating Devices

Rotating machines operate by exchanging angular momentum with the fluid. This energy transfer is often analyzed using the Euler pump/turbine equation, which relates the change in the fluid’s tangential (or swirl) velocity to the work done by or on the rotor. A net increase in the fluid’s tangential velocity typically indicates work being added, as in pumps, while a decrease implies energy extraction, characteristic of turbines.

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