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The lawn sprinkler with two jets, each located at 30 cm from the center. The jets are of 1 cm diameter. Assuming no friction, find the speed of the rotation for a discharge of 2.5 L/s.?
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The lawn sprinkler with two jets, each located at 30 cm from the cente...
Problem Statement:
A lawn sprinkler with two jets, each located at 30 cm from the center, is used to discharge water at a rate of 2.5 L/s. The jets have a diameter of 1 cm. Assuming no friction, we need to determine the speed of rotation for this sprinkler.
Solution:
Step 1: Convert the given discharge rate from L/s to m^3/s
Given discharge rate = 2.5 L/s
1 L = 0.001 m^3
Therefore, discharge rate = 2.5 L/s = 2.5 x 0.001 m^3/s = 0.0025 m^3/s
Step 2: Calculate the area of one jet
Radius of the jet = Diameter/2 = 1 cm / 2 = 0.5 cm = 0.005 m
Area of one jet = πr^2 = π(0.005)^2 = 0.00007854 m^2
Step 3: Calculate the velocity of the water jet
Discharge rate = Area x Velocity
0.0025 m^3/s = 0.00007854 m^2 x Velocity
Velocity = 0.0025 m^3/s / 0.00007854 m^2 = 31.848 m/s
Step 4: Calculate the angular velocity
Angular velocity (ω) = Velocity / Radius
Radius = 30 cm = 0.3 m (distance of the jets from the center)
ω = 31.848 m/s / 0.3 m = 106.16 rad/s
Conclusion:
The speed of rotation for the lawn sprinkler with two jets, each located at 30 cm from the center, for a discharge rate of 2.5 L/s is approximately 106.16 rad/s.
A lawn sprinkler with two jets, each located at 30 cm from the center, is used to discharge water at a rate of 2.5 L/s. The jets have a diameter of 1 cm. Assuming no friction, we need to determine the speed of rotation for this sprinkler.
Solution:
Step 1: Convert the given discharge rate from L/s to m^3/s
Given discharge rate = 2.5 L/s
1 L = 0.001 m^3
Therefore, discharge rate = 2.5 L/s = 2.5 x 0.001 m^3/s = 0.0025 m^3/s
Step 2: Calculate the area of one jet
Radius of the jet = Diameter/2 = 1 cm / 2 = 0.5 cm = 0.005 m
Area of one jet = πr^2 = π(0.005)^2 = 0.00007854 m^2
Step 3: Calculate the velocity of the water jet
Discharge rate = Area x Velocity
0.0025 m^3/s = 0.00007854 m^2 x Velocity
Velocity = 0.0025 m^3/s / 0.00007854 m^2 = 31.848 m/s
Step 4: Calculate the angular velocity
Angular velocity (ω) = Velocity / Radius
Radius = 30 cm = 0.3 m (distance of the jets from the center)
ω = 31.848 m/s / 0.3 m = 106.16 rad/s
Conclusion:
The speed of rotation for the lawn sprinkler with two jets, each located at 30 cm from the center, for a discharge rate of 2.5 L/s is approximately 106.16 rad/s.
Community Answer
The lawn sprinkler with two jets, each located at 30 cm from the cente...
50.67 rad/s
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The lawn sprinkler with two jets, each located at 30 cm from the center. The jets are of 1 cm diameter. Assuming no friction, find the speed of the rotation for a discharge of 2.5 L/s.?
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The lawn sprinkler with two jets, each located at 30 cm from the center. The jets are of 1 cm diameter. Assuming no friction, find the speed of the rotation for a discharge of 2.5 L/s.? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The lawn sprinkler with two jets, each located at 30 cm from the center. The jets are of 1 cm diameter. Assuming no friction, find the speed of the rotation for a discharge of 2.5 L/s.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lawn sprinkler with two jets, each located at 30 cm from the center. The jets are of 1 cm diameter. Assuming no friction, find the speed of the rotation for a discharge of 2.5 L/s.?.
The lawn sprinkler with two jets, each located at 30 cm from the center. The jets are of 1 cm diameter. Assuming no friction, find the speed of the rotation for a discharge of 2.5 L/s.? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The lawn sprinkler with two jets, each located at 30 cm from the center. The jets are of 1 cm diameter. Assuming no friction, find the speed of the rotation for a discharge of 2.5 L/s.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lawn sprinkler with two jets, each located at 30 cm from the center. The jets are of 1 cm diameter. Assuming no friction, find the speed of the rotation for a discharge of 2.5 L/s.?.
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