Project ForgeA test is conducted on a one-fifth scale model of a Francis turbine under a head of 2 m and volumetric flow rate of 1 m³/s at 450 rpm. Take the water density and the acceleration due to gravity as 10³ kg/m³ and 10 m/s², respectively. Assume no losses in either the model or the prototype turbine. The power (in MW) of a full sized turbine while working under a head of 30 m is __________ (correct to two decimal places).
Explanation
Dp/Dm=5 (prototype is 5× the model's linear size). Head coefficient similarity: Hp/Hm=(Np/Nm)²(Dp/Dm)² → 30/2=15=(Np/Nm)²×25 → Np/Nm=√0.6≈0.7746 → Np≈348.6 rpm. Flow coefficient similarity: Qp/Qm=(Np/Nm)(Dp/Dm)³=0.7746×125≈96.82 → Qp≈96.82 m³/s. With no losses, Pp=ρgQpHp=1000×10×96.82×30≈29.05×10⁶ W≈29.05 MW.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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