Project ForgeFluid Mechanics
Bernoulli's Equation
GATE 2016
Hard
An agitated vessel (Np=P/(ρn³D⁵), D=tank diameter/3) mixes at n=4rpm. In a scaled-up design (all linear dimensions doubled), power per unit volume is held constant, Np independent of Re. The impeller speed (rpm) for the same degree of mixing in the scaled-up vessel is
- A0.13
- B1.26
- 2.52
- D3.82
Explanation
P/V∝n³D⁵/L³∝n³L² (since D∝L,V∝L³). Constant P/V: n1³L1²=n2³(2L1)² ⟹ n2=n1/4^(1/3)=4/1.587=2.52 rpm.
Source: GATE CH 2016 (2016)
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