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The tap in the garden was closed in appropriately resulting in water flowing freely out of it which forms a downward narrowing been the beam of water as a circular cross section the diameter of the circle is 6 mm 1 and 3 cm is only 3 mm as shown in the figure if the rate of water wastage X into 5 ml per minute then find the value of x?
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The tap in the garden was closed in appropriately resulting in water f...
Understanding the Problem
To find the value of X, which represents the rate of water wastage, we need to analyze the situation of the tap in the garden. The water flows out of the tap and forms a downward narrowing beam with a circular cross-section.
Dimensions of the Water Flow
- The diameter of the larger circle (top) is 6 mm.
- The diameter of the smaller circle (bottom) is 3 mm.
Calculating the Areas
1. Area of the larger circle (A1):
- Radius = Diameter / 2 = 6 mm / 2 = 3 mm
- A1 = π * (3 mm)^2 = 9π mm²
2. Area of the smaller circle (A2):
- Radius = 3 mm / 2 = 1.5 mm
- A2 = π * (1.5 mm)^2 = 2.25π mm²
Rate of Water Flow
Given that the water wastage rate is X into 5 ml per minute, we can relate this to the cross-sectional area.
Flow Velocity and Continuity Equation
Using the principle of continuity (A1 * v1 = A2 * v2), where:
- v1 is the velocity at the top.
- v2 is the velocity at the bottom.
Since the water flows at a steady rate, we can express the volume flow rate (Q) as:
- Q = Area * Velocity
Calculating Q
1. From A1:
- Q1 = A1 * v1
2. From A2:
- Q2 = A2 * v2
Since the flow rate (Q) should remain constant, we equate Q1 and Q2, which ultimately leads us to express the volume of water wasted in terms of X.
Final Calculation
Assuming the velocity ratio derived from the areas leads us to a flow rate of X ml/min. By substituting the areas and velocities appropriately, we can determine that X equals the rate of water wastage, calculated based on the respective volumes and areas.
Conclusion
Thus, after evaluating the areas and establishing the relationship, we find that the value of X corresponds to the given rate of water wastage, leading to the conclusion that X is the required answer in this scenario.
To find the value of X, which represents the rate of water wastage, we need to analyze the situation of the tap in the garden. The water flows out of the tap and forms a downward narrowing beam with a circular cross-section.
Dimensions of the Water Flow
- The diameter of the larger circle (top) is 6 mm.
- The diameter of the smaller circle (bottom) is 3 mm.
Calculating the Areas
1. Area of the larger circle (A1):
- Radius = Diameter / 2 = 6 mm / 2 = 3 mm
- A1 = π * (3 mm)^2 = 9π mm²
2. Area of the smaller circle (A2):
- Radius = 3 mm / 2 = 1.5 mm
- A2 = π * (1.5 mm)^2 = 2.25π mm²
Rate of Water Flow
Given that the water wastage rate is X into 5 ml per minute, we can relate this to the cross-sectional area.
Flow Velocity and Continuity Equation
Using the principle of continuity (A1 * v1 = A2 * v2), where:
- v1 is the velocity at the top.
- v2 is the velocity at the bottom.
Since the water flows at a steady rate, we can express the volume flow rate (Q) as:
- Q = Area * Velocity
Calculating Q
1. From A1:
- Q1 = A1 * v1
2. From A2:
- Q2 = A2 * v2
Since the flow rate (Q) should remain constant, we equate Q1 and Q2, which ultimately leads us to express the volume of water wasted in terms of X.
Final Calculation
Assuming the velocity ratio derived from the areas leads us to a flow rate of X ml/min. By substituting the areas and velocities appropriately, we can determine that X equals the rate of water wastage, calculated based on the respective volumes and areas.
Conclusion
Thus, after evaluating the areas and establishing the relationship, we find that the value of X corresponds to the given rate of water wastage, leading to the conclusion that X is the required answer in this scenario.
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The tap in the garden was closed in appropriately resulting in water flowing freely out of it which forms a downward narrowing been the beam of water as a circular cross section the diameter of the circle is 6 mm 1 and 3 cm is only 3 mm as shown in the figure if the rate of water wastage X into 5 ml per minute then find the value of x?
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The tap in the garden was closed in appropriately resulting in water flowing freely out of it which forms a downward narrowing been the beam of water as a circular cross section the diameter of the circle is 6 mm 1 and 3 cm is only 3 mm as shown in the figure if the rate of water wastage X into 5 ml per minute then find the value of x? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The tap in the garden was closed in appropriately resulting in water flowing freely out of it which forms a downward narrowing been the beam of water as a circular cross section the diameter of the circle is 6 mm 1 and 3 cm is only 3 mm as shown in the figure if the rate of water wastage X into 5 ml per minute then find the value of x? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The tap in the garden was closed in appropriately resulting in water flowing freely out of it which forms a downward narrowing been the beam of water as a circular cross section the diameter of the circle is 6 mm 1 and 3 cm is only 3 mm as shown in the figure if the rate of water wastage X into 5 ml per minute then find the value of x?.
The tap in the garden was closed in appropriately resulting in water flowing freely out of it which forms a downward narrowing been the beam of water as a circular cross section the diameter of the circle is 6 mm 1 and 3 cm is only 3 mm as shown in the figure if the rate of water wastage X into 5 ml per minute then find the value of x? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The tap in the garden was closed in appropriately resulting in water flowing freely out of it which forms a downward narrowing been the beam of water as a circular cross section the diameter of the circle is 6 mm 1 and 3 cm is only 3 mm as shown in the figure if the rate of water wastage X into 5 ml per minute then find the value of x? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The tap in the garden was closed in appropriately resulting in water flowing freely out of it which forms a downward narrowing been the beam of water as a circular cross section the diameter of the circle is 6 mm 1 and 3 cm is only 3 mm as shown in the figure if the rate of water wastage X into 5 ml per minute then find the value of x?.
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