Roots blower: trend of efficiency with pressure ratio How does the efficiency of a Roots blower vary as the delivery pressure ratio is increased (other conditions unchanged)?

Introduction / Context:
Roots blowers are positive-displacement rotary machines that move nearly constant volume per revolution with internal backflow and leakage. They are often used for low pressure ratios where simplicity and robustness matter more than high efficiency.

Given Data / Assumptions:

• Fixed blower speed and geometry.
• Increasing delivery pressure ratio by throttling or backpressure.
• Air treated as a perfect gas; qualitative efficiency trend sought.

Concept / Approach:
In a Roots blower, actual compression largely occurs outside the casing when the trapped pocket opens to the high-pressure side, causing sudden backflow and mixing losses. As pressure ratio increases, internal leakage and pulsation losses represent a larger fraction of the indicated work, and the temperature rise increases, all of which reduce isentropic and overall efficiencies.

Step-by-Step Solution:

Verification / Alternative check:
Manufacturer performance maps show recommended operating ranges with pressure ratios typically below about 1.5–2, beyond which efficiency falls rapidly and discharge temperatures become excessive.

Why Other Options Are Wrong:

Increasing or unchanged efficiency contradicts both physics and empirical performance curves.A peaked trend is not characteristic for Roots blowers across the usual range; the dominant trend is downward.

Common Pitfalls:
Assuming Roots behave like dynamic compressors. They do not; they lack internal compression up to delivery pressure and thus suffer greater losses at higher ratios.

Final Answer:

decreases