A centrifugal compressor has an impeller tip speed of \(200\ \text{m/s}\). The whirl component of absolute velocity at the impeller exit is \(150\ \text{m/s}\). The whirl component of velocity at the inlet is zero. The specific heat at constant pressure is \(1\ \text{kJ/kg K}\). Using Euler's compressor principle, determine the temperature rise across the impeller.
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For centrifugal compressors,
\[
\boxed{
u\left(V_{w2}-V_{w1}\right)
=
C_p\Delta T.
}
\]
This relates the work input directly to the rise in stagnation temperature.