Question

Given a constant Power number, the power consumption of an agitator having geometric similarity but twice the diameter of a smaller agitator will consume ________ power at the same RPM as the smaller agitator.

• A. 4 times.
• B. 8 times.
• C. 16 times.
• D. 32 times.

Hint:

Power $\propto$ $D^5$. If Diameter is 2x, Power is $2^5 = 32$x.

Answer 1

The Correct Option is D

Step 1: Concept
The power consumption ($P$) of an agitator is determined by the Power Number ($N_p$) equation: $P = N_p \cdot \rho \cdot N^3 \cdot D^5$.

Step 2: Meaning
$\rho$ is density, $N$ is rotational speed (RPM), and $D$ is the diameter of the impeller.

Step 3: Analysis
Since $N_p$, $\rho$, and $N$ are constant, $P$ is proportional to $D^5$. If the diameter is doubled ($D_2 = 2D_1$), the new power is $P_2 \propto (2D_1)^5 = 32 D_1^5$.

Step 4: Conclusion
The power consumption increases by a factor of 32. which would correspond to a $D^4$ relationship, but $D^5$ is the standard for turbulent power consumption. Final Answer: (D)