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Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B?
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Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diamet...
**Solution:**
The problem can be solved by applying the Bernoulli's equation between sections A and B of the pipe.
**Bernoulli's Equation:**
Bernoulli's equation relates the pressure, velocity, and elevation of a fluid flowing in a pipe. It can be stated as:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Where,
P₁ and P₂ are the pressures at sections A and B respectively,
v₁ and v₂ are the velocities at sections A and B respectively,
ρ is the density of the fluid,
g is the acceleration due to gravity,
h₁ and h₂ are the elevations at sections A and B respectively.
Now, let's solve the problem step by step:
**Step 1: Convert Discharge to Velocity:**
Given, discharge = 60 liters/sec
To convert the discharge into velocity, we need to use the formula:
Q = Av
Where,
Q is the discharge,
A is the cross-sectional area of the pipe,
v is the velocity of the fluid.
Converting the discharge from liters/sec to cubic meters/sec:
60 liters/sec = 0.06 cubic meters/sec
Now, calculate the cross-sectional area of section A:
A₁ = πr₁² = π(0.15/2)² = 0.01767 square meters
Using the formula Q = Av, we can find the velocity at section A:
v₁ = Q/A₁ = 0.06/0.01767 = 3.394 m/s
**Step 2: Apply Bernoulli's Equation:**
Now, we can apply Bernoulli's equation between sections A and B:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Since the problem states that the flow is from A to B, the velocity at section B would be zero (v₂ = 0).
Also, the problem provides the elevation difference between the two sections (h₂ - h₁ = 3m).
Substituting the given values into the equation:
35kPa + ½ρ(3.394)² + ρ(9.81)(120) = P₂ + 0 + ρ(9.81)(130 + 3)
Simplifying the equation:
35kPa + ½ρ(3.394)² + ρ(9.81)(120) = P₂ + ρ(9.81)(133)
**Step 3: Solve for Pressure at Section B:**
We need the value of density (ρ) to solve the equation. However, the problem does not provide the fluid density.
Therefore, to solve for the pressure at section B, we need to know the fluid density or any other additional information related to the fluid properties.
Without the fluid density or any additional information, it is not possible to determine the pressure at section B.
Hence, the answer cannot be determined without additional information.
Note: It is important to have complete information about the fluid properties, such as density, to solve problems using the Bernoulli's equation accurately.
The problem can be solved by applying the Bernoulli's equation between sections A and B of the pipe.
**Bernoulli's Equation:**
Bernoulli's equation relates the pressure, velocity, and elevation of a fluid flowing in a pipe. It can be stated as:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Where,
P₁ and P₂ are the pressures at sections A and B respectively,
v₁ and v₂ are the velocities at sections A and B respectively,
ρ is the density of the fluid,
g is the acceleration due to gravity,
h₁ and h₂ are the elevations at sections A and B respectively.
Now, let's solve the problem step by step:
**Step 1: Convert Discharge to Velocity:**
Given, discharge = 60 liters/sec
To convert the discharge into velocity, we need to use the formula:
Q = Av
Where,
Q is the discharge,
A is the cross-sectional area of the pipe,
v is the velocity of the fluid.
Converting the discharge from liters/sec to cubic meters/sec:
60 liters/sec = 0.06 cubic meters/sec
Now, calculate the cross-sectional area of section A:
A₁ = πr₁² = π(0.15/2)² = 0.01767 square meters
Using the formula Q = Av, we can find the velocity at section A:
v₁ = Q/A₁ = 0.06/0.01767 = 3.394 m/s
**Step 2: Apply Bernoulli's Equation:**
Now, we can apply Bernoulli's equation between sections A and B:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Since the problem states that the flow is from A to B, the velocity at section B would be zero (v₂ = 0).
Also, the problem provides the elevation difference between the two sections (h₂ - h₁ = 3m).
Substituting the given values into the equation:
35kPa + ½ρ(3.394)² + ρ(9.81)(120) = P₂ + 0 + ρ(9.81)(130 + 3)
Simplifying the equation:
35kPa + ½ρ(3.394)² + ρ(9.81)(120) = P₂ + ρ(9.81)(133)
**Step 3: Solve for Pressure at Section B:**
We need the value of density (ρ) to solve the equation. However, the problem does not provide the fluid density.
Therefore, to solve for the pressure at section B, we need to know the fluid density or any other additional information related to the fluid properties.
Without the fluid density or any additional information, it is not possible to determine the pressure at section B.
Hence, the answer cannot be determined without additional information.
Note: It is important to have complete information about the fluid properties, such as density, to solve problems using the Bernoulli's equation accurately.
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Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B?
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Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B?.
Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B?.
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Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B?, a detailed solution for Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B? has been provided alongside types of Using bernoulli eqn. solve : A pipe has 2 sections A and B. The Diameter of A is 15cm and located at elevation of 120m and pressure observed at A is 35kPa. The section B is in elevation of 130m and diameter is equal to 30cm. The discharge through the pipe is equal to 60 liters per sec. The total energy loss recorded between two sections is equal to 3m. Find the pressure at section B when the flow is from A to B? theory, EduRev gives you an
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