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A jet of 50mm diameter impinges on a curved vane and is deflected through an angle of 175°. The vane moves in the sane direction as that of jet with a velocity of 35m/s . If the rate of flow is 170 LPS , determine the component of force on the vane in the direction of motion.also calculate power devloped by the vane and vane efficiency.?
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A jet of 50mm diameter impinges on a curved vane and is deflected thro...
Given Data
- Diameter of the jet (d) = 50 mm
- Radius of the jet (r) = d/2 = 25 mm = 0.025 m
- Velocity of the vane (V_v) = 35 m/s
- Angle of deflection (θ) = 175°
- Rate of flow (Q) = 170 LPS = 0.17 m³/s
Calculate Velocity of Jet
- Area of jet (A) = π * r² = π * (0.025)² = 0.0019635 m²
- Velocity of jet (V_j) = Q / A = 0.17 m³/s / 0.0019635 m² = 86.63 m/s
Force on the Vane
- Velocity of jet after deflection (V_j') = V_j * sin(θ) = 86.63 * sin(175°) = 86.63 * 0.9962 ≈ 86.32 m/s
- Change in momentum = (mass flow rate) * (V_j - V_j')
- Mass flow rate (ṁ) = Q * 1000 (kg/m³) = 0.17 * 1000 = 170 kg/s
- Change in momentum = 170 * (86.63 - 86.32) ≈ 170 * 0.31 = 52.7 N
Force Component in Direction of Motion
- The force component in the direction of motion (F) = Change in momentum = 52.7 N
Power Developed by the Vane
- Power (P) = F * V_v = 52.7 N * 35 m/s ≈ 1844.5 W or 1.844 kW
Vane Efficiency
- Efficiency (η) = (Power developed / Power input) * 100
- Power input = ṁ * (V_j² / 2) = 170 * (86.63² / 2) = 1271430 W
- η = (1844.5 / 1271430) * 100 ≈ 0.145%
Summary
- Force on the vane: 52.7 N
- Power developed: 1.844 kW
- Vane efficiency: 0.145%
This analysis provides a comprehensive view of the forces and power involved when a jet impinges on a curved vane.
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A jet of 50mm diameter impinges on a curved vane and is deflected through an angle of 175°. The vane moves in the sane direction as that of jet with a velocity of 35m/s . If the rate of flow is 170 LPS , determine the component of force on the vane in the direction of motion.also calculate power devloped by the vane and vane efficiency.?
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A jet of 50mm diameter impinges on a curved vane and is deflected through an angle of 175°. The vane moves in the sane direction as that of jet with a velocity of 35m/s . If the rate of flow is 170 LPS , determine the component of force on the vane in the direction of motion.also calculate power devloped by the vane and vane efficiency.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A jet of 50mm diameter impinges on a curved vane and is deflected through an angle of 175°. The vane moves in the sane direction as that of jet with a velocity of 35m/s . If the rate of flow is 170 LPS , determine the component of force on the vane in the direction of motion.also calculate power devloped by the vane and vane efficiency.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A jet of 50mm diameter impinges on a curved vane and is deflected through an angle of 175°. The vane moves in the sane direction as that of jet with a velocity of 35m/s . If the rate of flow is 170 LPS , determine the component of force on the vane in the direction of motion.also calculate power devloped by the vane and vane efficiency.?.
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