If there is no change in the fluid pressure between the inlet and outlet of the rotor of an axial flow machine, then degree of reaction (R)

Explanation:

Degree of Reaction (R) in Axial Flow Machines:

• The degree of reaction (R) in axial flow machines, such as turbines or compressors, is a dimensionless parameter that quantifies the proportion of the total energy transfer in the machine occurring due to the change in pressure (static enthalpy) relative to the total energy transfer (static + dynamic enthalpy). Mathematically, it is expressed as:

R = (Static Enthalpy Change)/(Total Enthalpy Change)

In simpler terms, the degree of reaction indicates the extent to which the energy transformation in the axial flow machine is due to a change in fluid pressure as opposed to the change in fluid velocity.

R = 0

• If there is no change in the fluid pressure between the inlet and outlet of the rotor, it implies that the static enthalpy change is zero. Since the degree of reaction (R) is defined as the ratio of static enthalpy change to total enthalpy change, the absence of pressure change results in:

R = (Static Enthalpy Change)/(Total Enthalpy Change) = 0

• This situation typically arises in machines where the energy transfer is entirely due to the change in fluid velocity (dynamic enthalpy), such as in purely impulse-based axial flow machines. In these machines, the rotor does not contribute to any pressure change, and all energy exchange is achieved through changes in fluid velocity.

Working Principle:

In axial flow machines with zero degree of reaction, the following principles apply:

• The pressure remains constant across the rotor, meaning no static enthalpy change occurs.
• The energy transfer is entirely due to the kinetic energy (dynamic enthalpy) of the fluid.
• The rotor blades are designed to alter the direction of the fluid flow without affecting its pressure.

Additional Information

To understand why the other options are incorrect, let’s analyze them:

Option 1: R > 0

This option implies that the degree of reaction is positive, meaning there is a pressure drop across the rotor. A positive degree of reaction is associated with machines where a significant portion of the energy transfer is due to a change in fluid pressure.

Option 2: R = 1

If R = 1, it indicates that the entire energy transfer in the machine is due to the change in fluid pressure, with no contribution from the change in fluid velocity. This condition corresponds to purely reaction-based machines, such as reaction turbines.

Option 3: R < 0

A negative degree of reaction would imply that the pressure increases across the rotor, which is an uncommon scenario in typical axial flow machines. In most cases, the rotor is designed to either maintain constant pressure (R = 0) or facilitate a pressure drop (R > 0).