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A solid shaft is designed to transmit 100 kW while rotating at N r.p.m. If the diameter of the shaft is doubled and is allowed to operate at 2 N r.p.m., the power that can be transmitted by the latter shaft is
- a)200 kW
- b)400 kW
- c)800 kW
- d)1600 kW
Correct answer is option 'D'. Can you explain this answer?
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A solid shaft is designed to transmit 100 kW while rotating at N r.p....
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A solid shaft is designed to transmit 100 kW while rotating at N r.p....
The power that can be transmitted by a shaft is determined by its diameter and rotational speed. To find the power transmitted by the latter shaft, we need to compare the original shaft with the doubled diameter and the 2N rotational speed.
1. Identify the given information:
- Power transmitted by the original shaft: 100 kW
- Rotational speed of the original shaft: N rpm
- Diameter of the original shaft: D
2. Determine the power transmitted by the original shaft:
- Power (P) = 100 kW
3. Determine the torque transmitted by the original shaft:
- Torque (T) = P / (2πN/60)
- Since the power is given in kilowatts (kW) and rotational speed in revolutions per minute (rpm), we need to convert the rotational speed to radians per second (rad/s). The conversion factor is (2π/60).
- T = 100 / (2πN/60) = (6000 / 2πN) Nm
4. Determine the torque transmitted by the latter shaft:
- Since the diameter of the latter shaft is doubled, the new diameter is 2D.
- Torque (T') = T (since torque is not affected by the diameter)
- T' = (6000 / 2πN) Nm
5. Determine the power transmitted by the latter shaft:
- The rotational speed of the latter shaft is 2N rpm.
- Power (P') = T' (2πN'/60)
- P' = (6000 / 2πN) (2π(2N)/60) = (6000 / 2πN) (4N/60) = (12000 / πN) Nm
6. Convert the power transmitted by the latter shaft to kilowatts:
- P' = (12000 / πN) Nm = (12000 / πN) (2πN/1000) kW = 24 kW
7. Simplify the expression:
- P' = 24 N kW
8. Substitute the value of N:
- P' = 24(2N) kW = 48N kW
9. Substitute the value of P:
- P' = 48(100) kW = 4800 kW
Therefore, the power that can be transmitted by the latter shaft is 4800 kW, which is equivalent to 1600 kW (option D).
1. Identify the given information:
- Power transmitted by the original shaft: 100 kW
- Rotational speed of the original shaft: N rpm
- Diameter of the original shaft: D
2. Determine the power transmitted by the original shaft:
- Power (P) = 100 kW
3. Determine the torque transmitted by the original shaft:
- Torque (T) = P / (2πN/60)
- Since the power is given in kilowatts (kW) and rotational speed in revolutions per minute (rpm), we need to convert the rotational speed to radians per second (rad/s). The conversion factor is (2π/60).
- T = 100 / (2πN/60) = (6000 / 2πN) Nm
4. Determine the torque transmitted by the latter shaft:
- Since the diameter of the latter shaft is doubled, the new diameter is 2D.
- Torque (T') = T (since torque is not affected by the diameter)
- T' = (6000 / 2πN) Nm
5. Determine the power transmitted by the latter shaft:
- The rotational speed of the latter shaft is 2N rpm.
- Power (P') = T' (2πN'/60)
- P' = (6000 / 2πN) (2π(2N)/60) = (6000 / 2πN) (4N/60) = (12000 / πN) Nm
6. Convert the power transmitted by the latter shaft to kilowatts:
- P' = (12000 / πN) Nm = (12000 / πN) (2πN/1000) kW = 24 kW
7. Simplify the expression:
- P' = 24 N kW
8. Substitute the value of N:
- P' = 24(2N) kW = 48N kW
9. Substitute the value of P:
- P' = 48(100) kW = 4800 kW
Therefore, the power that can be transmitted by the latter shaft is 4800 kW, which is equivalent to 1600 kW (option D).
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A solid shaft is designed to transmit 100 kW while rotating at N r.p.m. If the diameter of the shaft is doubled and is allowed to operate at 2 N r.p.m., the power that can be transmitted by the latter shaft isa)200 kWb)400 kWc)800 kWd)1600 kWCorrect answer is option 'D'. Can you explain this answer?
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