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Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.
Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer?
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Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadil...
Ρ = 888 kg⁄m3 μ = 0.8 kg⁄m d = 5 cm or r = 2.5 cm
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L = 40 m Hagen Poiseuille formula
Most Upvoted Answer
Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadil...
Given data:
- Oil temperature = 20°C
- Oil density = 888 kg/m³
- Oil viscosity = 0.800 kg/m∙s
- Pipe diameter = 5 cm
- Pipe length = 40 m
- Inlet pressure = 745 kPa
- Outlet pressure = 97 kPa
Assumptions:
- Steady flow
- Incompressible fluid
- Horizontal pipe
To determine the flow rate of oil through the pipe, we can use the Bernoulli's equation and the Darcy-Weisbach equation.
1. Bernoulli's equation:
P₁ + (1/2)ρV₁² + ρgh₁ = P₂ + (1/2)ρV₂² + ρgh₂
where:
- P₁ and P₂ are the pressures at inlet and outlet, respectively
- V₁ and V₂ are the velocities at inlet and outlet, respectively
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h₁ and h₂ are the elevations at inlet and outlet, respectively
Since the pipe is horizontal, h₁ = h₂. Also, the elevation difference between the two points is negligible compared to the length of the pipe, so we can neglect the last term. Therefore, the Bernoulli's equation reduces to:
P₁ + (1/2)ρV₁² = P₂ + (1/2)ρV₂²
2. Darcy-Weisbach equation:
hf = (fL/D)(V²/2g)
where:
- hf is the head loss due to friction
- f is the friction factor
- L is the length of the pipe
- D is the diameter of the pipe
- V is the velocity of the fluid
- g is the acceleration due to gravity
The head loss due to friction can be expressed as:
hf = (4fL/D)(V²/2g)
Since the flow is steady, the flow rate (Q) can be expressed as:
Q = AV
where:
- A is the cross-sectional area of the pipe
3. Solution:
We can use the above equations to solve for the flow rate (Q).
From the Bernoulli's equation:
V₁ = √[(2(P₁ - P₂))/ρ]
From the Darcy-Weisbach equation:
hf = (4fL/D)(V²/2g)
Substituting V = Q/A, we get:
hf = (4fLQ²)/(2gAD²)
Equating the head loss due to friction to the pressure drop between inlet and outlet, we get:
hf = (P₁ - P₂)/(ρg)
Substituting the above equations and simplifying, we get:
Q = (π/4)D²√[(2g/ρ)(P₁ - P₂)/(fL/D + D/3.7)]
where:
- π is the constant pi (3.14159...)
- D is the diameter of the pipe
- g is the acceleration due to gravity
- ρ is the density of the fluid
- P₁ and P₂ are the pressures at inlet and outlet, respectively
- L is the length of the pipe
- f is the friction factor (which depends on the Reynolds number)
- Reynolds number =
- Oil temperature = 20°C
- Oil density = 888 kg/m³
- Oil viscosity = 0.800 kg/m∙s
- Pipe diameter = 5 cm
- Pipe length = 40 m
- Inlet pressure = 745 kPa
- Outlet pressure = 97 kPa
Assumptions:
- Steady flow
- Incompressible fluid
- Horizontal pipe
To determine the flow rate of oil through the pipe, we can use the Bernoulli's equation and the Darcy-Weisbach equation.
1. Bernoulli's equation:
P₁ + (1/2)ρV₁² + ρgh₁ = P₂ + (1/2)ρV₂² + ρgh₂
where:
- P₁ and P₂ are the pressures at inlet and outlet, respectively
- V₁ and V₂ are the velocities at inlet and outlet, respectively
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h₁ and h₂ are the elevations at inlet and outlet, respectively
Since the pipe is horizontal, h₁ = h₂. Also, the elevation difference between the two points is negligible compared to the length of the pipe, so we can neglect the last term. Therefore, the Bernoulli's equation reduces to:
P₁ + (1/2)ρV₁² = P₂ + (1/2)ρV₂²
2. Darcy-Weisbach equation:
hf = (fL/D)(V²/2g)
where:
- hf is the head loss due to friction
- f is the friction factor
- L is the length of the pipe
- D is the diameter of the pipe
- V is the velocity of the fluid
- g is the acceleration due to gravity
The head loss due to friction can be expressed as:
hf = (4fL/D)(V²/2g)
Since the flow is steady, the flow rate (Q) can be expressed as:
Q = AV
where:
- A is the cross-sectional area of the pipe
3. Solution:
We can use the above equations to solve for the flow rate (Q).
From the Bernoulli's equation:
V₁ = √[(2(P₁ - P₂))/ρ]
From the Darcy-Weisbach equation:
hf = (4fL/D)(V²/2g)
Substituting V = Q/A, we get:
hf = (4fLQ²)/(2gAD²)
Equating the head loss due to friction to the pressure drop between inlet and outlet, we get:
hf = (P₁ - P₂)/(ρg)
Substituting the above equations and simplifying, we get:
Q = (π/4)D²√[(2g/ρ)(P₁ - P₂)/(fL/D + D/3.7)]
where:
- π is the constant pi (3.14159...)
- D is the diameter of the pipe
- g is the acceleration due to gravity
- ρ is the density of the fluid
- P₁ and P₂ are the pressures at inlet and outlet, respectively
- L is the length of the pipe
- f is the friction factor (which depends on the Reynolds number)
- Reynolds number =
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Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer?
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Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer?.
Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer?.
Solutions for Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer?, a detailed solution for Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer? has been provided alongside types of Oil at 20°C (ρ = 888 kg⁄m3 and μ = 0.800 kg/m ∙ s) is flowing steadily through a 5 cm diameter, 40 m long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kPa, respectively. Determine the flow rate of oil (in L/s) through the pipe assuming the pipe is horizontal.Correct answer is 'Range: 3.00 to 3.2'. Can you explain this answer? theory, EduRev gives you an
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