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Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.?
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Water flows at a rate of 0.07 m3/min through a flanged faucet with a p...
Given:
- Flow rate of water: 0.07 m3/min
- Inner diameter of the pipe at the flange: 198 mm
- Pressure at the flange: 0.896 bar (gauge)
- Total weight of the faucet assembly + water: 57 N
To Find:
- Net force on the flange
Assumptions:
- The flow of water is steady and incompressible.
- The height difference between the inlet and outlet of the pipe is negligible.
- The pressure at the outlet of the pipe is atmospheric (0 bar gauge).
Solution:
Step 1: Convert Units
- Convert the flow rate from m3/min to m3/s:
- 0.07 m3/min = 0.07/60 m3/s = 0.00117 m3/s
- Convert the inner diameter of the pipe from mm to m:
- 198 mm = 198/1000 m = 0.198 m
Step 2: Calculate the Velocity of Water
- The flow rate can be expressed as the product of the cross-sectional area and the velocity of the water:
- Flow rate = Cross-sectional area × Velocity
- Rearranging the formula, we can solve for the velocity of the water:
- Velocity = Flow rate / Cross-sectional area
- The cross-sectional area of the pipe can be calculated using the formula for the area of a circle:
- Cross-sectional area = π × (Diameter/2)2
- Substituting the given values, we can calculate the velocity of the water:
- Cross-sectional area = π × (0.198/2)2 = 0.0309 m2
- Velocity = 0.00117 m3/s / 0.0309 m2 = 0.0378 m/s
Step 3: Calculate the Force Exerted by Water
- The force exerted by the water can be calculated using the formula:
- Force = Pressure × Area
- The area can be calculated using the formula for the area of a circle:
- Area = π × (Diameter/2)2
- Substituting the given values, we can calculate the force exerted by the water:
- Area = π × (0.198/2)2 = 0.0309 m2
- Force = 0.896 bar × 0.0309 m2 = 0.0276 N
Step 4: Calculate the Net Force on the Flange
- The net force on the flange can be calculated by subtracting the weight of the faucet assembly plus water from the force exerted by the water:
- Net Force = Force - Weight
- Substituting the given values, we can calculate the net force on the flange:
- Net Force = 0.0276 N - 57 N = -56.9724 N
Answer:
The net force on the flange is approximately -56.9724 N.
- Flow rate of water: 0.07 m3/min
- Inner diameter of the pipe at the flange: 198 mm
- Pressure at the flange: 0.896 bar (gauge)
- Total weight of the faucet assembly + water: 57 N
To Find:
- Net force on the flange
Assumptions:
- The flow of water is steady and incompressible.
- The height difference between the inlet and outlet of the pipe is negligible.
- The pressure at the outlet of the pipe is atmospheric (0 bar gauge).
Solution:
Step 1: Convert Units
- Convert the flow rate from m3/min to m3/s:
- 0.07 m3/min = 0.07/60 m3/s = 0.00117 m3/s
- Convert the inner diameter of the pipe from mm to m:
- 198 mm = 198/1000 m = 0.198 m
Step 2: Calculate the Velocity of Water
- The flow rate can be expressed as the product of the cross-sectional area and the velocity of the water:
- Flow rate = Cross-sectional area × Velocity
- Rearranging the formula, we can solve for the velocity of the water:
- Velocity = Flow rate / Cross-sectional area
- The cross-sectional area of the pipe can be calculated using the formula for the area of a circle:
- Cross-sectional area = π × (Diameter/2)2
- Substituting the given values, we can calculate the velocity of the water:
- Cross-sectional area = π × (0.198/2)2 = 0.0309 m2
- Velocity = 0.00117 m3/s / 0.0309 m2 = 0.0378 m/s
Step 3: Calculate the Force Exerted by Water
- The force exerted by the water can be calculated using the formula:
- Force = Pressure × Area
- The area can be calculated using the formula for the area of a circle:
- Area = π × (Diameter/2)2
- Substituting the given values, we can calculate the force exerted by the water:
- Area = π × (0.198/2)2 = 0.0309 m2
- Force = 0.896 bar × 0.0309 m2 = 0.0276 N
Step 4: Calculate the Net Force on the Flange
- The net force on the flange can be calculated by subtracting the weight of the faucet assembly plus water from the force exerted by the water:
- Net Force = Force - Weight
- Substituting the given values, we can calculate the net force on the flange:
- Net Force = 0.0276 N - 57 N = -56.9724 N
Answer:
The net force on the flange is approximately -56.9724 N.
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Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.?
Question Description
Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.?.
Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.?.
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Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.?, a detailed solution for Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.? has been provided alongside types of Water flows at a rate of 0.07 m3/min through a flanged faucet with a partially closed gate valve spigot. The inner diameter of the pipe at the location of the flange is 198 mm, and the pressure at that location is measured to be 0.896 bar (gauge). The total weight of the faucet assembly plus the water within it is 57 N. Calculate the net force on the flange.? theory, EduRev gives you an
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