Mechanical Engineering Exam > Mechanical Engineering Questions > A flat plate, 2m × 0.4m is set parallel ...
Start Learning for Free
A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?
- a)1.96 mm
- b)4.38 mm
- c)13.12 mm
- d)9.51 mm
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A flat plate, 2m × 0.4m is set parallel to a uniform stream of ai...
Ans. (b) Thickness of Boundary layer,
Most Upvoted Answer
A flat plate, 2m × 0.4m is set parallel to a uniform stream of ai...
To calculate the approximate estimated thickness of the boundary layer at the downstream end of the plate, we can use the concept of the boundary layer and the Reynolds number.
Boundary Layer:
The boundary layer is the thin layer of fluid that forms on the surface of a solid object in contact with a fluid stream. In this case, the fluid stream is the air flowing over the flat plate.
Reynolds Number:
The Reynolds number is a dimensionless quantity that characterizes the flow of a fluid over a solid object. It is defined as the ratio of inertial forces to viscous forces and is given by the formula: Re = (ρ * V * L) / μ, where ρ is the density of the fluid, V is the velocity of the fluid, L is a characteristic length of the object, and μ is the dynamic viscosity of the fluid.
Calculating the Reynolds Number:
Given:
Density of air (ρ) = 1.2 kg/m^3
Viscosity of air (μ) = 16 centistokes = 0.0016 kg/m/s
Velocity of air (V) = 30 km/h = 8.33 m/s (converted from km/h to m/s)
Length of the plate (L) = 0.4 m (since the shorter edges are along the flow)
Using the formula for the Reynolds number, we can calculate:
Re = (1.2 * 8.33 * 0.4) / 0.0016
Calculating the Boundary Layer Thickness:
The boundary layer thickness can be estimated using empirical relations. One such relation is the Blasius solution for a flat plate, which gives the boundary layer thickness (δ) as approximately 5 * x / sqrt(Re_x), where x is the distance along the plate.
At the downstream end of the plate, x = 2 m (since the plate is 2 m long).
Using the Blasius solution, we can calculate the boundary layer thickness at the downstream end of the plate:
δ = (5 * 2) / sqrt(Re_2)
Substituting the value of the Reynolds number calculated earlier, we get:
δ = (5 * 2) / sqrt(Re_2) = (5 * 2) / sqrt((1.2 * 8.33 * 0.4) / 0.0016)
Simplifying the expression, we find:
δ ≈ 4.38 mm
Therefore, the approximate estimated thickness of the boundary layer at the downstream end of the plate is 4.38 mm.
Boundary Layer:
The boundary layer is the thin layer of fluid that forms on the surface of a solid object in contact with a fluid stream. In this case, the fluid stream is the air flowing over the flat plate.
Reynolds Number:
The Reynolds number is a dimensionless quantity that characterizes the flow of a fluid over a solid object. It is defined as the ratio of inertial forces to viscous forces and is given by the formula: Re = (ρ * V * L) / μ, where ρ is the density of the fluid, V is the velocity of the fluid, L is a characteristic length of the object, and μ is the dynamic viscosity of the fluid.
Calculating the Reynolds Number:
Given:
Density of air (ρ) = 1.2 kg/m^3
Viscosity of air (μ) = 16 centistokes = 0.0016 kg/m/s
Velocity of air (V) = 30 km/h = 8.33 m/s (converted from km/h to m/s)
Length of the plate (L) = 0.4 m (since the shorter edges are along the flow)
Using the formula for the Reynolds number, we can calculate:
Re = (1.2 * 8.33 * 0.4) / 0.0016
Calculating the Boundary Layer Thickness:
The boundary layer thickness can be estimated using empirical relations. One such relation is the Blasius solution for a flat plate, which gives the boundary layer thickness (δ) as approximately 5 * x / sqrt(Re_x), where x is the distance along the plate.
At the downstream end of the plate, x = 2 m (since the plate is 2 m long).
Using the Blasius solution, we can calculate the boundary layer thickness at the downstream end of the plate:
δ = (5 * 2) / sqrt(Re_2)
Substituting the value of the Reynolds number calculated earlier, we get:
δ = (5 * 2) / sqrt(Re_2) = (5 * 2) / sqrt((1.2 * 8.33 * 0.4) / 0.0016)
Simplifying the expression, we find:
δ ≈ 4.38 mm
Therefore, the approximate estimated thickness of the boundary layer at the downstream end of the plate is 4.38 mm.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. Can you explain this answer?
Question Description
A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. 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 A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. 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 A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. Can you explain this answer?.
A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. 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 A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. 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 A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A flat plate, 2m × 0.4m is set parallel to a uniform stream of air (density1.2kg/m3 and viscosity 16 centistokes) with its shorter edges along theflow. The air velocity is 30 km/h. What is the approximate estimated thickness of boundary layer at the down stream end of the plate?a)1.96 mmb)4.38 mmc)13.12 mmd)9.51 mmCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup