# DBT JRF 2022 — Question 96

Exam: DBT JRF 2022 · Section: B · Topic: Bioprocess Engineering › Bioreactor Agitation & Shear Rate · Difficulty: Medium

## Question

You wish to reduce the maximum shear rate in your reactor (given by impeller tip speed), without changing the power consumption (agitator power). For this, you will:

## Options

- **A.** Increase the diameter of impeller and reduce the RPM
- **B.** Reduce the diameter of impeller and increase the RPM
- **C.** Reduce RPM only
- **D.** Reduce diameter of impeller only

## Answer

Option A

## Explanation

Bioreactor impeller scale-up: decrease tip speed, maintain power: Tip speed = $\pi \cdot D \cdot N$ where D = impeller diameter, N = rotational speed. Power consumption $\propto N^3 D^5$ (for turbulent regime, Power number is constant). To DECREASE tip speed while KEEPING power CONSTANT: Let new diameter $D' = kD$ (increase D) and new speed $N' = N/m$ (decrease N). From tip speed: $\pi D' N' = \pi D N \cdot \frac{k}{m}$ . To decrease tip speed: $\frac{k}{m} < 1$ . From power: $(N')^3 (D')^5 = \left(\frac{N}{m}\right)^3 (kD)^5 = \frac{k^5}{m^3} N^3 D^5 =$ constant → $\frac{k^5}{m^3} = 1$ → $k^5 = m^3$ . Solution: INCREASE D (larger impeller) and DECREASE N (slower rotation) such that $k^5 = m^3$ . Result: Tip speed decreases (less shear), power is maintained (same mixing energy), but shear is gentler — important for shear-sensitive cells (mammalian, insect cells). Answer: Increase impeller diameter D and decrease rotation speed N to decrease tip speed while maintaining power constant.

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