Fig.F-23

Fig.F-24

only at one particular flow rate for a given rotor speed. This flow rate corresponds to the design operation point in Fig.22b. At a different flow rate or different speed, the misalignment loss occurs, as explained for the rotor blades in Fig.F-24. Analogical misalignment occurs also at the entrance to the stator blading. This loss increases quadratically with the flow deviation from the design flow rate. It may be decreased by using articulated blades with variable entrance angle (in a similar manner as shown for the reverse flow direction in the turbine articulated stator blading in Fig.F-25) adjusted to momentary operating conditions. This, however, increases the price of the machine considerably and is usually justifiable only in case of the largest turbomachines. Moreover, such an adjustment cannot be but an approximate one.
The increase of energy of fluid during its passage through the rotor as derived in Fig.F-14 and re-written on the previous page may be written also as

using the decomposition of velocity vectors into the radial and tangential components, Fig.F-18. In general, the passage between the rotor blades may have an inlined inlet - so that the inlet angle of the relative
Leonhard Euler
Born: 15 April 1707 in Basel, Switzerland
Died: 18 Sept 1783 in St Petersburg, Russia
--------------------------------------------------
Euler's father wanted his son
to follow him into the church and
sent him to the University of Basel
to prepare for the ministry. However
geometry soon became his favourite
subject. Euler obtained his father's
consent to change to mathematics after
Johann Bernoulli had used his persuasion.
Johann Bernoulli became his teacher.
Euler joined the St. Petersburg Academy
of Science in 1727, two years after it was
founded by Catherine I the wife of Peter
the Great. Euler served as a medical
lieutenant in the Russian navy from 1727
to 1730. In St Petersburg he lived with
Daniel Bernoulli. He became professor of
physics at the academy in 1730 and professor
of mathematics in 1733. He married and left
Johann Bernoulli's house in 1733.
velocity vector is , cf. Fig.F-17. In that case, it might be necessary do subtract from the resultant value the term , derived in a similar manner. The resultant expression

This formula is the Euler Turbine Theorem, derived already in 1754, long time before appearance of first turbomechines. It should be said, however, that the blades at the rotor entrance location are usually designed (by suitably selecting their angle so that fluid enters the rotor without rotation - then the term disappears.



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This is page Nr. F09 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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