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Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40cm and depth 24cm?
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Water flows at the rate of 10 metre per minute from a cylindrical pipe...
Step 1: Calculate the Volume of the Conical Vessel
To find the time required to fill the conical vessel, we first need to calculate its volume.
- The formula for the volume of a cone is:
Volume = (1/3) * π * r² * h
- Given:
- Diameter at the base = 40 cm, so radius (r) = 20 cm = 0.2 m
- Height (h) = 24 cm = 0.24 m
- Now, substituting the values into the formula:
Volume = (1/3) * π * (0.2)² * (0.24)
Volume ≈ (1/3) * 3.14 * 0.04 * 0.24
Volume ≈ 0.0314 m³
Step 2: Calculate the Flow Rate of Water
Next, we need to find the volumetric flow rate of water from the pipe.
- The diameter of the pipe = 5 mm = 0.005 m, so radius (r) = 0.0025 m
- The area (A) of the pipe is calculated as:
A = π * (0.0025)²
A ≈ 1.9635 x 10^-5 m²
- The flow rate (Q) can be calculated as:
Q = Area * velocity
Q = A * 10 m/min (convert 10 m/min to m/s = 10/60 m/s)
Q ≈ 1.9635 x 10^-5 * (10/60)
Q ≈ 3.2725 x 10^-6 m³/s
Step 3: Calculate the Time to Fill the Vessel
Finally, we find the time taken to fill the conical vessel.
- Time (t) = Volume / Flow rate
- t = 0.0314 m³ / (3.2725 x 10^-6 m³/s)
- t ≈ 9600 seconds
- Converting seconds to minutes: 9600 / 60 = 160 minutes.
Conclusion
It will take approximately 160 minutes to fill the conical vessel.
To find the time required to fill the conical vessel, we first need to calculate its volume.
- The formula for the volume of a cone is:
Volume = (1/3) * π * r² * h
- Given:
- Diameter at the base = 40 cm, so radius (r) = 20 cm = 0.2 m
- Height (h) = 24 cm = 0.24 m
- Now, substituting the values into the formula:
Volume = (1/3) * π * (0.2)² * (0.24)
Volume ≈ (1/3) * 3.14 * 0.04 * 0.24
Volume ≈ 0.0314 m³
Step 2: Calculate the Flow Rate of Water
Next, we need to find the volumetric flow rate of water from the pipe.
- The diameter of the pipe = 5 mm = 0.005 m, so radius (r) = 0.0025 m
- The area (A) of the pipe is calculated as:
A = π * (0.0025)²
A ≈ 1.9635 x 10^-5 m²
- The flow rate (Q) can be calculated as:
Q = Area * velocity
Q = A * 10 m/min (convert 10 m/min to m/s = 10/60 m/s)
Q ≈ 1.9635 x 10^-5 * (10/60)
Q ≈ 3.2725 x 10^-6 m³/s
Step 3: Calculate the Time to Fill the Vessel
Finally, we find the time taken to fill the conical vessel.
- Time (t) = Volume / Flow rate
- t = 0.0314 m³ / (3.2725 x 10^-6 m³/s)
- t ≈ 9600 seconds
- Converting seconds to minutes: 9600 / 60 = 160 minutes.
Conclusion
It will take approximately 160 minutes to fill the conical vessel.
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Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40cm and depth 24cm?
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Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40cm and depth 24cm? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40cm and depth 24cm? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40cm and depth 24cm?.
Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40cm and depth 24cm? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40cm and depth 24cm? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40cm and depth 24cm?.
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