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Water flows through a cylindrical pipe of internal diameter 7 cm at 2 m per second. If the pipe is always half full, then what is the volume of water (in litres) discharged in 10 minutes?
- a)2310
- b)3850
- c)4620
- d)9240
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Water flows through a cylindrical pipe of internal diameter 7 cm at 2 ...
Volume of water flown in 1sec = ( 22/7 x 7/2 x 7/2 x 200) cm3 = 7700 cm3
Volume of water flown in 10 min = (7700 x 60 x 10) cm3
= ( 7700 x 60 x 10/1000 ) litres = 4620 litres
Volume of water flown in 10 min = (7700 x 60 x 10) cm3
= ( 7700 x 60 x 10/1000 ) litres = 4620 litres
Most Upvoted Answer
Water flows through a cylindrical pipe of internal diameter 7 cm at 2 ...
Given:
- Internal diameter of the cylindrical pipe = 7 cm
- Water flows through the pipe at a speed of 2 m/s
- The pipe is always half full
- Time = 10 minutes
To find:
- Volume of water discharged in 10 minutes
Assumptions:
- The cylindrical pipe is of uniform cross-section and the flow of water is steady.
- The pipe is completely filled with water and the water level remains constant.
Formula:
- The volume of a cylinder = πr²h, where r is the radius of the cylinder and h is the height or length of the cylinder.
Solution:
Step 1: Convert the internal diameter into radius
- The internal diameter of the pipe = 7 cm
- Radius = diameter/2 = 7/2 = 3.5 cm
Step 2: Convert the radius from cm to meters
- 1 meter = 100 cm
- Radius in meters = 3.5/100 = 0.035 m
Step 3: Calculate the cross-sectional area of the pipe
- The cross-sectional area of a pipe = πr², where r is the radius of the pipe
- Cross-sectional area = π(0.035)² = 0.00385 m²
Step 4: Calculate the volume of water discharged per second
- The flow rate of water = 2 m/s
- Volume of water discharged per second = flow rate × cross-sectional area
- Volume of water discharged per second = 2 × 0.00385 = 0.0077 m³/s
Step 5: Convert the volume from cubic meters to liters
- 1 cubic meter = 1000 liters
- Volume of water discharged per second in liters = 0.0077 × 1000 = 7.7 liters/s
Step 6: Calculate the volume of water discharged in 10 minutes
- Time = 10 minutes = 10 × 60 = 600 seconds
- Volume of water discharged in 10 minutes = volume per second × time in seconds
- Volume of water discharged in 10 minutes = 7.7 × 600 = 4620 liters
Hence, the volume of water discharged in 10 minutes is 4620 liters. Therefore, option C is the correct answer.
- Internal diameter of the cylindrical pipe = 7 cm
- Water flows through the pipe at a speed of 2 m/s
- The pipe is always half full
- Time = 10 minutes
To find:
- Volume of water discharged in 10 minutes
Assumptions:
- The cylindrical pipe is of uniform cross-section and the flow of water is steady.
- The pipe is completely filled with water and the water level remains constant.
Formula:
- The volume of a cylinder = πr²h, where r is the radius of the cylinder and h is the height or length of the cylinder.
Solution:
Step 1: Convert the internal diameter into radius
- The internal diameter of the pipe = 7 cm
- Radius = diameter/2 = 7/2 = 3.5 cm
Step 2: Convert the radius from cm to meters
- 1 meter = 100 cm
- Radius in meters = 3.5/100 = 0.035 m
Step 3: Calculate the cross-sectional area of the pipe
- The cross-sectional area of a pipe = πr², where r is the radius of the pipe
- Cross-sectional area = π(0.035)² = 0.00385 m²
Step 4: Calculate the volume of water discharged per second
- The flow rate of water = 2 m/s
- Volume of water discharged per second = flow rate × cross-sectional area
- Volume of water discharged per second = 2 × 0.00385 = 0.0077 m³/s
Step 5: Convert the volume from cubic meters to liters
- 1 cubic meter = 1000 liters
- Volume of water discharged per second in liters = 0.0077 × 1000 = 7.7 liters/s
Step 6: Calculate the volume of water discharged in 10 minutes
- Time = 10 minutes = 10 × 60 = 600 seconds
- Volume of water discharged in 10 minutes = volume per second × time in seconds
- Volume of water discharged in 10 minutes = 7.7 × 600 = 4620 liters
Hence, the volume of water discharged in 10 minutes is 4620 liters. Therefore, option C is the correct answer.
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Water flows through a cylindrical pipe of internal diameter 7 cm at 2 m per second. If the pipe is always half full, then what is the volume of water (in litres) discharged in 10 minutes?a)2310b)3850c)4620d)9240Correct answer is option 'C'. Can you explain this answer?
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