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A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at other end B. The pipe is 3m long, is inclined to horizontal at an angle a = tan¹ (1/4) with end A above B. If the flow velocity at section B is 0.6 m/s, determine the difference of pressure between the two sections.?
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A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at ot...
Problem Statement
A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at other end B. The pipe is 3m long, is inclined to horizontal at an angle a = tan¹ (1/4) with end A above B. If the flow velocity at section B is 0.6 m/s, determine the difference of pressure between the two sections.
Solution
Given:
- Diameter of end A = 20cm
- Diameter of end B = 10cm
- Length of pipe = 3m
- Inclination angle = tan¹ (1/4)
- Flow velocity at section B = 0.6m/s
Step 1: Calculate the inclination of the pipe
Inclination angle, a = tan¹ (1/4)
a = 14.04°
Step 2: Calculate the velocity of flow at section A
We know that the volume of fluid flowing through the pipe is constant. Hence,
Volume of fluid flowing through section A = Volume of fluid flowing through section B
π/4 x d₁² x V₁ = π/4 x d₂² x V₂
where,
- d₁ = Diameter of end A = 20cm
- d₂ = Diameter of end B = 10cm
- V₂ = Velocity of flow at section B = 0.6m/s
Substituting the values, we get
π/4 x 0.2² x V₁ = π/4 x 0.1² x 0.6
V₁ = 3.6m/s
Step 3: Calculate the pressure difference between section A and B
Using Bernoulli's equation,
P₁ + ρgh₁ + 1/2 ρV₁² = P₂ + ρgh₂ + 1/2 ρV₂²
where,
- P₁ = Pressure at section A
- P₂ = Pressure at section B
- ρ = Density of fluid
- g = Acceleration due to gravity
- h₁ = Height of section A from reference level
- h₂ = Height of section B from reference level
Assuming the reference level at section B, we have
h₁ = 3m x sin(14.04°) = 0.76m
h₂ = 0m
Also, as the fluid is incompressible, the density is constant. Hence,
P₁ + 1/2 ρV₁² + ρgh₁ = P₂ + 1/2 ρV₂² + ρgh₂
P₁ - P₂
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A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at other end B. The pipe is 3m long, is inclined to horizontal at an angle a = tan¹ (1/4) with end A above B. If the flow velocity at section B is 0.6 m/s, determine the difference of pressure between the two sections.?
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A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at other end B. The pipe is 3m long, is inclined to horizontal at an angle a = tan¹ (1/4) with end A above B. If the flow velocity at section B is 0.6 m/s, determine the difference of pressure between the two sections.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at other end B. The pipe is 3m long, is inclined to horizontal at an angle a = tan¹ (1/4) with end A above B. If the flow velocity at section B is 0.6 m/s, determine the difference of pressure between the two sections.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at other end B. The pipe is 3m long, is inclined to horizontal at an angle a = tan¹ (1/4) with end A above B. If the flow velocity at section B is 0.6 m/s, determine the difference of pressure between the two sections.?.
A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at other end B. The pipe is 3m long, is inclined to horizontal at an angle a = tan¹ (1/4) with end A above B. If the flow velocity at section B is 0.6 m/s, determine the difference of pressure between the two sections.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at other end B. The pipe is 3m long, is inclined to horizontal at an angle a = tan¹ (1/4) with end A above B. If the flow velocity at section B is 0.6 m/s, determine the difference of pressure between the two sections.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform tapering pipe is 20 cm diameter at one end A and 10 cm at other end B. The pipe is 3m long, is inclined to horizontal at an angle a = tan¹ (1/4) with end A above B. If the flow velocity at section B is 0.6 m/s, determine the difference of pressure between the two sections.?.
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