Question:
A hydraulic turbine with rotor diameter of 100 mm produces 200 W of power while rotating at 300 rpm. Another dynamically-similar turbine rotates at a speed of 1500 rpm. Consider both turbines to operate with the same fluid (identical density and viscosity), and neglect any gravitational effect. Then the power (in W, rounded off to nearest integer) produced by the second turbine is $________________$.
A hydraulic turbine with rotor diameter of 100 mm produces 200 W of power while rotating at 300 rpm. Another dynamically-similar turbine rotates at a speed of 1500 rpm. Consider both turbines to operate with the same fluid (identical density and viscosity), and neglect any gravitational effect. Then the power (in W, rounded off to nearest integer) produced by the second turbine is $________________$.
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In turbomachinery, power is proportional to $N^3 D^5$ when dynamic similarity holds.
Updated On: Aug 29, 2025
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Correct Answer: 430
Solution and Explanation
Step 1: Recall similarity law.
For turbines, under dynamic similarity: \[ \frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^3 \left(\frac{D_2}{D_1}\right)^5 \]
Step 2: Write given data.
$D_1 = D_2 = 100$ mm (same diameter)
$P_1 = 200$ W, $N_1 = 300$ rpm
$N_2 = 1500$ rpm
Step 3: Apply formula.
\[ \frac{P_2}{200} = \left(\frac{1500}{300}\right)^3 = (5)^3 = 125 \] \[ P_2 = 200 \times 125 = 25000 \ \text{W} \] Final Answer: \[ \boxed{25000 \ \text{W}} \]
For turbines, under dynamic similarity: \[ \frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^3 \left(\frac{D_2}{D_1}\right)^5 \]
Step 2: Write given data.
$D_1 = D_2 = 100$ mm (same diameter)
$P_1 = 200$ W, $N_1 = 300$ rpm
$N_2 = 1500$ rpm
Step 3: Apply formula.
\[ \frac{P_2}{200} = \left(\frac{1500}{300}\right)^3 = (5)^3 = 125 \] \[ P_2 = 200 \times 125 = 25000 \ \text{W} \] Final Answer: \[ \boxed{25000 \ \text{W}} \]
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