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Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)?
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Jet of water having a velocity of 35 m/sec impinges on a series of van...
Solution:
Velocity Triangle:
The velocity triangle is a diagram used to understand and analyze the flow of fluids through machines. It shows the velocities of the fluid at the inlet and outlet of the machine and the velocity of the machine itself.
Angles of Vanes Tips:
The angles of the vanes tips are important because they determine whether the water entering and leaving the vanes will do so without any shock. This is important because shock can cause damage to the vanes and reduce the efficiency of the machine.
- The angle of the vane tips at the inlet should be equal to the angle between the direction of motion of the vanes and the jet of water.
- In this case, the angle of the vane tips at the inlet should be 30°.
- The angle of the vane tips at the outlet should be equal to the sum of the angle between the direction of motion of the vanes and the jet of water and the angle between the direction of motion of the vanes and the direction of the water leaving the vanes.
- In this case, the angle of the vane tips at the outlet should be 150°.
Work Done per Unit Weight of Water:
The work done per unit weight of water is the energy that is transferred from the water to the vanes as the water flows through the machine. This energy is used to turn the vanes and perform work.
- The work done per unit weight of water can be calculated using the following equation: W = U2 - U1 + (V2^2 - V1^2)/2g
- Where W is the work done per unit weight of water, U1 and U2 are the velocities of the vanes at the inlet and outlet respectively, V1 and V2 are the velocities of the water at the inlet and outlet respectively, and g is the acceleration due to gravity.
- In this case, U1 = 20 m/s, U2 = 20 m/s, V1 = 35 m/s, V2 = 20 m/s, and g = 9.81 m/s^2.
- Plugging these values into the equation, we get W = -32.6 J/kg.
Efficiency:
The efficiency of the machine is the ratio of the work output to the work input. In this case, the work output is the work done per unit weight of water and the work input is the kinetic energy of the water entering the machine.
- The kinetic energy of the water entering the machine can be calculated using the following equation: KE = V1^2/2g
- Where KE is the kinetic energy of the water entering the machine, V1 is the velocity of the water at the inlet, and g is the acceleration due to gravity.
- In this case, V1 = 35 m/s and g = 9.81 m/s^2.
- Plugging these values into the equation, we get KE = 625.4 J/kg.
- Therefore, the efficiency of the machine is W/KE = -32.6/625.4 = -0.052 or 5.2%.
Conclusion:
In conclusion, we have analyzed the flow of water through a machine using velocity triangles and calculated the angles of the vane tips, the work done per unit weight of water, and the efficiency of the machine. The angle of the vane tips at the inlet should be 30° and at the
Velocity Triangle:
The velocity triangle is a diagram used to understand and analyze the flow of fluids through machines. It shows the velocities of the fluid at the inlet and outlet of the machine and the velocity of the machine itself.
Angles of Vanes Tips:
The angles of the vanes tips are important because they determine whether the water entering and leaving the vanes will do so without any shock. This is important because shock can cause damage to the vanes and reduce the efficiency of the machine.
- The angle of the vane tips at the inlet should be equal to the angle between the direction of motion of the vanes and the jet of water.
- In this case, the angle of the vane tips at the inlet should be 30°.
- The angle of the vane tips at the outlet should be equal to the sum of the angle between the direction of motion of the vanes and the jet of water and the angle between the direction of motion of the vanes and the direction of the water leaving the vanes.
- In this case, the angle of the vane tips at the outlet should be 150°.
Work Done per Unit Weight of Water:
The work done per unit weight of water is the energy that is transferred from the water to the vanes as the water flows through the machine. This energy is used to turn the vanes and perform work.
- The work done per unit weight of water can be calculated using the following equation: W = U2 - U1 + (V2^2 - V1^2)/2g
- Where W is the work done per unit weight of water, U1 and U2 are the velocities of the vanes at the inlet and outlet respectively, V1 and V2 are the velocities of the water at the inlet and outlet respectively, and g is the acceleration due to gravity.
- In this case, U1 = 20 m/s, U2 = 20 m/s, V1 = 35 m/s, V2 = 20 m/s, and g = 9.81 m/s^2.
- Plugging these values into the equation, we get W = -32.6 J/kg.
Efficiency:
The efficiency of the machine is the ratio of the work output to the work input. In this case, the work output is the work done per unit weight of water and the work input is the kinetic energy of the water entering the machine.
- The kinetic energy of the water entering the machine can be calculated using the following equation: KE = V1^2/2g
- Where KE is the kinetic energy of the water entering the machine, V1 is the velocity of the water at the inlet, and g is the acceleration due to gravity.
- In this case, V1 = 35 m/s and g = 9.81 m/s^2.
- Plugging these values into the equation, we get KE = 625.4 J/kg.
- Therefore, the efficiency of the machine is W/KE = -32.6/625.4 = -0.052 or 5.2%.
Conclusion:
In conclusion, we have analyzed the flow of water through a machine using velocity triangles and calculated the angles of the vane tips, the work done per unit weight of water, and the efficiency of the machine. The angle of the vane tips at the inlet should be 30° and at the
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Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)?
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Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)?.
Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)?.
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Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)?, a detailed solution for Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)? has been provided alongside types of Jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity of 20 m/sec. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw velocity triangles and calculate: (a) The angles of vanes tips so water enters and leaves without shock (b) The work done per unit weight of water entering the vanes. (c) The efficiency (pg 1112)? theory, EduRev gives you an
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