GATE AE 2018 • Q64 NAT • 2 Marks Propulsion

Propulsion

Compressors and Turbines

Subtopic: Centrifugal Compressors

Question Statement:

The relative velocity of air leaving a straight radial impeller of a centrifugal compressor is 100 m/s. If the impeller tip speed is 200 m/s, for a slip free operation, the absolute velocity (in m/s) of air at the impeller exit is _________ (accurate to one decimal place).

Official Answer Key:

223.5

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2018 Q.64 / AE Q.54)** **1. Intuitive Physical Setup & Given Parameters**: - Straight radial impeller blades: the blade angle at exit is $\beta_2 = 90^\circ$ (purely radial relative exit velocity). - Relative velocity at exit: $W_2 = 100\text{ m/s}$ (in the radial direction, $C_{r2} = W_2 = 100\text{ m/s}$). - Impeller tip speed: $U_2 = 200\text{ m/s}$. - Slip-free operation: Slip factor $\sigma = 1.0 \implies C_{w2} = U_2 = 200\text{ m/s}$. **2. Step-by-Step Mathematical Derivation**: 1. **Exit Velocity Components**: - Radial component of absolute velocity: C_{r2} = W_2 = 100\text{ m/s} - Tangential (whirl) component of absolute velocity: C_{w2} = U_2 = 200\text{ m/s} 2. **Resultant Absolute Exit Velocity ($C_2$)**: Since the radial and tangential components are mutually perpendicular: C_2 = \sqrt{C_{r2}^2 + C_{w2}^2} = \sqrt{(100)^2 + (200)^2} = \sqrt{10000 + 40000} = \sqrt{50000} C_2 = 100 \sqrt{5} \approx 100 \times 2.236068 = 223.61\text{ m/s} Rounding to one decimal place: C_2 \approx 223.6\text{ m/s} This falls perfectly in the center of the official acceptable interval **[222.0, 225.0]**. **3. Comprehensive Options & Distractor Analysis**: - **Question Type**: Numerical Answer Type (NAT). - **Official Range**: **222.0 to 225.0 m/s**. **4. Official Master Key & Exam Takeaway**: - **Official Answer**: **223.5** (Acceptable Range: **222.0 to 225.0**) - **Key Formula**: For straight radial vanes with zero slip: $C_2 = \sqrt{W_2^2 + U_2^2} = \sqrt{100^2 + 200^2} \approx 223.6\text{ m/s}$.
← Previous (Q63) All 2018 Questions Next (Q65) →

Related Compressors and Turbines Solved Questions

View All Compressors and Turbines PYQs →
GATE AE 2026 Q18 MCQ • 1M

The figure below depicts two ideal gas turbine cycles, cycle 1-2-3-4-1 and cycle 1-2-3'-4'-1, on a T-s diagram. Which one the following statements is FALSE?
GATE AE 2026 Q27 MSQ • 1M

The figure below shows the blading of the rotors of two different axial turbomachines under their typical operating conditions, labelled as Configuration I and Configuration II. Which of the following statements is/are TRUE?
GATE AE 2026 Q28 MSQ • 1M

A multi-stage axial compressor can be operated at two points, A and B, both of which lie on the same speed line, as shown in the figure below. If $\eta$ is the isentropic efficiency of the compressor, select the statements that is/are TRUE.
GATE AE 2026 Q42 MCQ • 2M

The figure below shows a compressor stage with station numbers 1, 2, and 3 as indicated. If p0i, T0i, and Ci refer to the average values of total pressure, total temperature, and absolute flow speed, respectively, at the ith station, select the CORRECT option considering losses.

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test