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Two horizontal pipes of different diameters are connected together by a valve.Their diameters are 3 cm and 9cm.Water flows at speed 6 ms-¹ in the first pipe and the pressure in it is 200000Nm-².find the water pressure and speed in second pipe.?
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Two horizontal pipes of different diameters are connected together by ...
Given:
- Diameter of the first pipe (D1) = 3 cm
- Diameter of the second pipe (D2) = 9 cm
- Speed of water in the first pipe (V1) = 6 m/s
- Pressure in the first pipe (P1) = 200,000 N/m²
To find:
- Water pressure in the second pipe (P2)
- Speed of water in the second pipe (V2)
Explanation:
1. Understanding Flow Rate:
The flow rate of a fluid through a pipe is given by the equation:
Q = A * V
Where:
- Q is the flow rate (volume of fluid passing through a point per unit time)
- A is the cross-sectional area of the pipe
- V is the velocity of the fluid
2. Relationship between Velocity and Cross-sectional Area:
The cross-sectional area of a pipe is related to its diameter by the equation:
A = π * (D/2)²
Where:
- A is the cross-sectional area
- D is the diameter of the pipe
3. Applying the Equations:
3.1. Flow Rate in the First Pipe:
The flow rate in the first pipe can be calculated using the equation:
Q1 = A1 * V1
3.2. Relationship between the Cross-sectional Areas:
The cross-sectional area of the first pipe (A1) and the second pipe (A2) can be related by the equation:
A1/A2 = (D1/2)² / (D2/2)²
3.3. Flow Rate in the Second Pipe:
Using the relationship between the cross-sectional areas, we can rewrite the flow rate equation for the second pipe as:
Q2 = Q1 * (A2/A1)
4. Relationship between Pressure and Flow Rate:
The pressure (P) in a fluid can be related to the flow rate (Q) by the equation:
P = ρ * g * h + 1/2 * ρ * V²
Where:
- P is the pressure
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the height of the fluid column
5. Applying the Pressure Equation:
5.1. Pressure in the First Pipe:
The pressure in the first pipe can be calculated using the equation:
P1 = 1/2 * ρ * V1²
5.2. Pressure in the Second Pipe:
Using the flow rate relationship (Q2 = Q1 * (A2/A1)), we can rewrite the pressure equation for the second pipe as:
P2 = 1/2 * ρ * V2²
6. Solving for Pressure and Speed:
6.1. Pressure in the Second Pipe (P2):
Since the density (ρ) and acceleration due to gravity (g) are constant, the pressure in the second pipe can be found using the ratio of the flow rates:
P2 = P1 * (Q2/Q1)
6.2. Speed in the Second Pipe (V2):
Using
- Diameter of the first pipe (D1) = 3 cm
- Diameter of the second pipe (D2) = 9 cm
- Speed of water in the first pipe (V1) = 6 m/s
- Pressure in the first pipe (P1) = 200,000 N/m²
To find:
- Water pressure in the second pipe (P2)
- Speed of water in the second pipe (V2)
Explanation:
1. Understanding Flow Rate:
The flow rate of a fluid through a pipe is given by the equation:
Q = A * V
Where:
- Q is the flow rate (volume of fluid passing through a point per unit time)
- A is the cross-sectional area of the pipe
- V is the velocity of the fluid
2. Relationship between Velocity and Cross-sectional Area:
The cross-sectional area of a pipe is related to its diameter by the equation:
A = π * (D/2)²
Where:
- A is the cross-sectional area
- D is the diameter of the pipe
3. Applying the Equations:
3.1. Flow Rate in the First Pipe:
The flow rate in the first pipe can be calculated using the equation:
Q1 = A1 * V1
3.2. Relationship between the Cross-sectional Areas:
The cross-sectional area of the first pipe (A1) and the second pipe (A2) can be related by the equation:
A1/A2 = (D1/2)² / (D2/2)²
3.3. Flow Rate in the Second Pipe:
Using the relationship between the cross-sectional areas, we can rewrite the flow rate equation for the second pipe as:
Q2 = Q1 * (A2/A1)
4. Relationship between Pressure and Flow Rate:
The pressure (P) in a fluid can be related to the flow rate (Q) by the equation:
P = ρ * g * h + 1/2 * ρ * V²
Where:
- P is the pressure
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the height of the fluid column
5. Applying the Pressure Equation:
5.1. Pressure in the First Pipe:
The pressure in the first pipe can be calculated using the equation:
P1 = 1/2 * ρ * V1²
5.2. Pressure in the Second Pipe:
Using the flow rate relationship (Q2 = Q1 * (A2/A1)), we can rewrite the pressure equation for the second pipe as:
P2 = 1/2 * ρ * V2²
6. Solving for Pressure and Speed:
6.1. Pressure in the Second Pipe (P2):
Since the density (ρ) and acceleration due to gravity (g) are constant, the pressure in the second pipe can be found using the ratio of the flow rates:
P2 = P1 * (Q2/Q1)
6.2. Speed in the Second Pipe (V2):
Using
Community Answer
Two horizontal pipes of different diameters are connected together by ...
Use equation of continuity and then Bernoulli's formula
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Two horizontal pipes of different diameters are connected together by a valve.Their diameters are 3 cm and 9cm.Water flows at speed 6 ms-¹ in the first pipe and the pressure in it is 200000Nm-².find the water pressure and speed in second pipe.?
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Two horizontal pipes of different diameters are connected together by a valve.Their diameters are 3 cm and 9cm.Water flows at speed 6 ms-¹ in the first pipe and the pressure in it is 200000Nm-².find the water pressure and speed in second pipe.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two horizontal pipes of different diameters are connected together by a valve.Their diameters are 3 cm and 9cm.Water flows at speed 6 ms-¹ in the first pipe and the pressure in it is 200000Nm-².find the water pressure and speed in second pipe.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two horizontal pipes of different diameters are connected together by a valve.Their diameters are 3 cm and 9cm.Water flows at speed 6 ms-¹ in the first pipe and the pressure in it is 200000Nm-².find the water pressure and speed in second pipe.?.
Two horizontal pipes of different diameters are connected together by a valve.Their diameters are 3 cm and 9cm.Water flows at speed 6 ms-¹ in the first pipe and the pressure in it is 200000Nm-².find the water pressure and speed in second pipe.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two horizontal pipes of different diameters are connected together by a valve.Their diameters are 3 cm and 9cm.Water flows at speed 6 ms-¹ in the first pipe and the pressure in it is 200000Nm-².find the water pressure and speed in second pipe.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two horizontal pipes of different diameters are connected together by a valve.Their diameters are 3 cm and 9cm.Water flows at speed 6 ms-¹ in the first pipe and the pressure in it is 200000Nm-².find the water pressure and speed in second pipe.?.
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