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Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)
Correct answer is '12.1'. Can you explain this answer?
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Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing th...
Reynolds number for this flow,
Re = 811.5 < />
Hence, the flow is laminar and friction factor for this Re is,
f = 64/Re = 64/811.5 = 0.07887
Then the pressure drop per unit length, (L = 1 m)
= 12.1 kPa
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Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing th...
Given data:
- Temperature (T) = 40°C = 313.15 K
- Density (ρ) = 1252 kg/m3
- Dynamic viscosity (μ) = 0.27 kg/ms
- Diameter of the pipe (D) = 5 cm = 0.05 m
- Average velocity (V) = 3.5 m/s
To find:
Pressure drop (ΔP) per unit length of the pipe
Assumptions:
- The flow is steady and fully developed.
- The flow is incompressible.
- The pipe is horizontal, smooth, and of constant diameter.
- The fluid is Newtonian.
Calculations:
Step 1: Calculate the Reynolds number (Re) using the formula:
Re = (ρVD) / μ
Given:
ρ = 1252 kg/m3
V = 3.5 m/s
D = 0.05 m
μ = 0.27 kg/ms
Substituting the values, we get:
Re = (1252 kg/m3 × 3.5 m/s × 0.05 m) / 0.27 kg/ms
Re ≈ 2433.33
Step 2: Determine the flow regime based on the Reynolds number (Re).
For flow in a smooth pipe, the flow regime can be categorized as:
- Laminar flow (Re < />
- Transitional flow (2000 < re="" />< />
- Turbulent flow (Re > 4000)
In this case, Re ≈ 2433.33, which falls within the laminar flow regime.
Step 3: Calculate the pressure drop per unit length of the pipe (ΔP/L) using the Hagen-Poiseuille equation for laminar flow:
ΔP/L = (32μVL) / (πD4)
Given:
μ = 0.27 kg/ms
V = 3.5 m/s
L = 1 m (unit length of the pipe)
D = 0.05 m
Substituting the values, we get:
ΔP/L = (32 × 0.27 kg/ms × 3.5 m/s × 1 m) / (π × (0.05 m)4)
ΔP/L ≈ 12.1 kPa
Answer:
The pressure drop per unit length of the pipe is approximately 12.1 kPa.
- Temperature (T) = 40°C = 313.15 K
- Density (ρ) = 1252 kg/m3
- Dynamic viscosity (μ) = 0.27 kg/ms
- Diameter of the pipe (D) = 5 cm = 0.05 m
- Average velocity (V) = 3.5 m/s
To find:
Pressure drop (ΔP) per unit length of the pipe
Assumptions:
- The flow is steady and fully developed.
- The flow is incompressible.
- The pipe is horizontal, smooth, and of constant diameter.
- The fluid is Newtonian.
Calculations:
Step 1: Calculate the Reynolds number (Re) using the formula:
Re = (ρVD) / μ
Given:
ρ = 1252 kg/m3
V = 3.5 m/s
D = 0.05 m
μ = 0.27 kg/ms
Substituting the values, we get:
Re = (1252 kg/m3 × 3.5 m/s × 0.05 m) / 0.27 kg/ms
Re ≈ 2433.33
Step 2: Determine the flow regime based on the Reynolds number (Re).
For flow in a smooth pipe, the flow regime can be categorized as:
- Laminar flow (Re < />
- Transitional flow (2000 < re="" />< />
- Turbulent flow (Re > 4000)
In this case, Re ≈ 2433.33, which falls within the laminar flow regime.
Step 3: Calculate the pressure drop per unit length of the pipe (ΔP/L) using the Hagen-Poiseuille equation for laminar flow:
ΔP/L = (32μVL) / (πD4)
Given:
μ = 0.27 kg/ms
V = 3.5 m/s
L = 1 m (unit length of the pipe)
D = 0.05 m
Substituting the values, we get:
ΔP/L = (32 × 0.27 kg/ms × 3.5 m/s × 1 m) / (π × (0.05 m)4)
ΔP/L ≈ 12.1 kPa
Answer:
The pressure drop per unit length of the pipe is approximately 12.1 kPa.
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Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer?
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Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer?.
Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer?.
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Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer?, a detailed solution for Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer? has been provided alongside types of Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/ms is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s. What will be the pressure drop (kPa) per unit length of the pipe? (Answer up to one decimal place)Correct answer is '12.1'. Can you explain this answer? theory, EduRev gives you an
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