Fluid mechanical property
Rothalpy (or trothalpy) formula_1, a short name of rotational stagnation enthalpy, is a fluid mechanical property of importance in the study of flow within rotating systems.
Concept.
Consider we have an inertial frame of reference formula_2 and a rotating frame of reference formula_3 which both are sharing common origin formula_4. Assume that frame formula_3 is rotating around a fixed axis with angular velocity formula_6. Now assuming fluid velocity to be formula_7 and fluid velocity relative to rotating frame of reference to be formula_8:
Rothalpy of a fluid point formula_9 can be defined as
formula_10
where formula_11 and formula_12 and formula_13 is the stagnation enthalpy of fluid point formula_9 relative to the rotating frame of reference formula_3, which is given by
formula_16
and is known as relative stagnation enthalpy.
Rothalpy can also be defined in terms of absolute stagnation enthalpy:
formula_17
where formula_18 is tangential component of fluid velocity formula_7.
Applications.
Rothalpy has applications in turbomachinery and study of relative flows in rotating systems.
One such application is that for steady, adiabatic and irreversible flow in a turbomachine, the value of rothalpy across a blade remains constant along a flow streamline:
formula_20
so Euler equation of turbomachinery can be written in terms of rothalpy.
This form of the Euler work equation shows that, for rotating blade rows, the relative stagnation enthalpy is constant through the blades provided the blade speed is constant. In other words, formula_21, if the radius of a streamline passing through the blades stays the same. This result is important for analyzing turbomachinery flows in the relative frame of reference.
Naming.
The function formula_1 was first introduced by Wu (1952) and has acquired the widely used name rothalpy.
This quantity is commonly called rothalpy, a compound word combining the terms rotation and enthalpy. However, its construction does not conform to the established rules for formation of new words in the English language, namely, that the roots of the new word originate from the same language. The word trothalpy satisfies this requirement as trohos is the Greek root for wheel and enthalpy is to put heat in, whereas rotation is derived from Latin rotare.