Problem 10.17 [Difficulty: 1]
Given: Impulse turbibe
Find: Optimum speed using the Euler turbomachine equation
Solution:
The governing equation is the Euler turbomachine equation
In terms of the notation of Example 10.13, for a stationary CV
r1r2
RU1U2
UVt1 VU Vt2 VU( ) cos θ() and mflow ρQ
Hence Tshaft RV U()cos θ()RV U()[]ρQ Tout Tshaft
ρQRVU()1 cos θ()()
The power is Wout ωTout
ρQRωVU()1 cos θ()() Wout ρQUVU()1 cos θ()()
These results are identical to those of Example 10.13. The proof that maximum power is when U = V/2 is hence also the same
and will not be repeated here.