Project ForgeFluid Mechanics
Bernoulli's Equation
GATE 2019
Hard
A disk turbine stirs liquid in a baffled tank. Lab model: D1=0.05m, N1=600rpm, μ1=0.001 Pa·s, ρ1=1000 kg/m³. Actual: D2=0.5m, N2=600rpm, μ2=0.1 Pa·s, ρ2=1000 kg/m³ (gravity negligible). If P1, P2 are the powers required, the ratio P2/P1 is
- A10^3
- B10^4
- 10^5
- D10^6
Explanation
Re1=ρN D1²/μ1=1000×10×0.0025/0.001=25000. Re2=ρN D2²/μ2=1000×10×0.25/0.1=25000. Since Re1=Re2, the power number Np(Re) is identical for both. P=Np·ρN³D⁵, so P2/P1=(D2/D1)⁵=10⁵.
Source: GATE CH 2019 (2019)
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