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1. The velocity distribution for flow over a flat plate is given by u = 3/2y - y^3/2 , Where u is the point velocity in meter per second at a distance y meter above the plate. Determine the shear stress at y = 9 cm. Assume dynamic viscosity as 8 poise .?
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1. The velocity distribution for flow over a flat plate is given by u ...
Shear Stress Calculation for Flow over a Flat Plate
Given:
- Velocity distribution: u = (3/2)y - y^(3/2)
- Distance from the plate: y = 9 cm
- Dynamic viscosity: 8 poise
Shear Stress Formula:
The shear stress (τ) can be calculated using the formula:
τ = μ * du/dy
where:
- τ is the shear stress
- μ is the dynamic viscosity
- du/dy is the derivative of the velocity distribution with respect to y
To determine the shear stress at y = 9 cm, we need to calculate the derivative du/dy first.
Derivative Calculation:
The velocity distribution equation is u = (3/2)y - y^(3/2). To find du/dy, we differentiate this equation with respect to y.
du/dy = d/dy[(3/2)y - y^(3/2)]
Applying the power rule of differentiation, we get:
du/dy = (3/2) - (3/2)(3/2)y^(-1/2)
Simplifying further, we have:
du/dy = (3/2) - (9/4)y^(-1/2)
Shear Stress Calculation:
Now that we have the derivative du/dy, we can calculate the shear stress at y = 9 cm using the shear stress formula.
τ = μ * du/dy
Plugging in the given values:
τ = 8 * [(3/2) - (9/4)(9^(-1/2))]
Calculating further:
τ = 8 * [(3/2) - (9/4)(1/3)]
τ = 8 * [(3/2) - (3/4)]
τ = 8 * [(6/4) - (3/4)]
τ = 8 * (3/4)
τ = 6 poise
Result:
The shear stress at y = 9 cm is 6 poise.
Given:
- Velocity distribution: u = (3/2)y - y^(3/2)
- Distance from the plate: y = 9 cm
- Dynamic viscosity: 8 poise
Shear Stress Formula:
The shear stress (τ) can be calculated using the formula:
τ = μ * du/dy
where:
- τ is the shear stress
- μ is the dynamic viscosity
- du/dy is the derivative of the velocity distribution with respect to y
To determine the shear stress at y = 9 cm, we need to calculate the derivative du/dy first.
Derivative Calculation:
The velocity distribution equation is u = (3/2)y - y^(3/2). To find du/dy, we differentiate this equation with respect to y.
du/dy = d/dy[(3/2)y - y^(3/2)]
Applying the power rule of differentiation, we get:
du/dy = (3/2) - (3/2)(3/2)y^(-1/2)
Simplifying further, we have:
du/dy = (3/2) - (9/4)y^(-1/2)
Shear Stress Calculation:
Now that we have the derivative du/dy, we can calculate the shear stress at y = 9 cm using the shear stress formula.
τ = μ * du/dy
Plugging in the given values:
τ = 8 * [(3/2) - (9/4)(9^(-1/2))]
Calculating further:
τ = 8 * [(3/2) - (9/4)(1/3)]
τ = 8 * [(3/2) - (3/4)]
τ = 8 * [(6/4) - (3/4)]
τ = 8 * (3/4)
τ = 6 poise
Result:
The shear stress at y = 9 cm is 6 poise.
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1. The velocity distribution for flow over a flat plate is given by u = 3/2y - y^3/2 , Where u is the point velocity in meter per second at a distance y meter above the plate. Determine the shear stress at y = 9 cm. Assume dynamic viscosity as 8 poise .?
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1. The velocity distribution for flow over a flat plate is given by u = 3/2y - y^3/2 , Where u is the point velocity in meter per second at a distance y meter above the plate. Determine the shear stress at y = 9 cm. Assume dynamic viscosity as 8 poise .? 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 1. The velocity distribution for flow over a flat plate is given by u = 3/2y - y^3/2 , Where u is the point velocity in meter per second at a distance y meter above the plate. Determine the shear stress at y = 9 cm. Assume dynamic viscosity as 8 poise .? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. The velocity distribution for flow over a flat plate is given by u = 3/2y - y^3/2 , Where u is the point velocity in meter per second at a distance y meter above the plate. Determine the shear stress at y = 9 cm. Assume dynamic viscosity as 8 poise .?.
1. The velocity distribution for flow over a flat plate is given by u = 3/2y - y^3/2 , Where u is the point velocity in meter per second at a distance y meter above the plate. Determine the shear stress at y = 9 cm. Assume dynamic viscosity as 8 poise .? 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 1. The velocity distribution for flow over a flat plate is given by u = 3/2y - y^3/2 , Where u is the point velocity in meter per second at a distance y meter above the plate. Determine the shear stress at y = 9 cm. Assume dynamic viscosity as 8 poise .? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. The velocity distribution for flow over a flat plate is given by u = 3/2y - y^3/2 , Where u is the point velocity in meter per second at a distance y meter above the plate. Determine the shear stress at y = 9 cm. Assume dynamic viscosity as 8 poise .?.
Solutions for 1. The velocity distribution for flow over a flat plate is given by u = 3/2y - y^3/2 , Where u is the point velocity in meter per second at a distance y meter above the plate. Determine the shear stress at y = 9 cm. Assume dynamic viscosity as 8 poise .? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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