GATE 2026 AE – Question 61
A centrifugal compressor has a constant-width radial diffuser. The diameters at the diffuser inlet and outlet are 0.2 m and 0.3 m, respectively. The flow at the diffuser inlet and outlet is assumed to be steady and uniform. The average velocity at the diffuser inlet and outlet are $(60\,\hat e_r + 75\,\hat e_\theta)$ m/s and $(u\,\hat e_r + 50\,\hat e_\theta)$ m/s, respectively. If the flow through the diffuser is treated as steady and incompressible, the value of $u$ is ________ (rounded off to the nearest integer).
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Correct answer: 40
Explanation
For steady incompressible flow with constant width $b$, the volume flow is the same at both radii: $v_{r,1}(\pi D_1 b) = v_{r,2}(\pi D_2 b)$, so $u = 60 \times \frac{0.2}{0.3} = 40$ m/s. The tangential velocity does not enter the continuity equation.