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Calculate the friction drag on a plate 0.5 m × 0.2 m placed longitudinally in a stream of oil (specific gravity 0.9 and kinematic viscosity 1 stokes) flowing with a free stream velocity of 6 m/s. Also, calculate the boundary layer thickness and shear stress at the middle of the plate. Compare average shear stress with shear stress at the trailing edge.?
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Calculate the friction drag on a plate 0.5 m × 0.2 m placed longitudin...
Calculation of Friction Drag

  • Given, the plate dimensions are 0.5 m × 0.2 m

  • The specific gravity of oil is 0.9

  • The kinematic viscosity of oil is 1 stokes

  • The free stream velocity of oil is 6 m/s


The formula for calculating friction drag is:

Friction drag = 0.5 x ρ x V^2 x Cd x A


  • ρ = density of fluid = specific gravity x density of water = 0.9 x 1000 = 900 kg/m^3

  • V = free stream velocity = 6 m/s

  • Cd = drag coefficient for a flat plate = 1.328

  • A = surface area of the plate = 0.5 x 0.2 = 0.1 m^2


Putting the given values in the formula, we get:

Friction drag = 0.5 x 900 x 6^2 x 1.328 x 0.1 = 142.3 N


Calculation of Boundary Layer Thickness and Shear Stress

  • The thickness of the boundary layer can be calculated using the formula:

    • δ = 5.0 x x/√Re_x

  • Where x is the distance from the leading edge of the plate

  • Re_x = Reynolds number at distance x

  • Re_x = ρ x V x x/μ

  • Where μ is dynamic viscosity = ρ x kinematic viscosity = 900 x 10^-6 = 0.0009 Pa.s

  • Putting the values, we get:

    • Re_x = 900 x 6 x x/0.0009 = 54,000x

  • At the middle of the plate, x = 0.25 m

  • Therefore, Re_x = 13,500

  • Putting the values in the formula for boundary layer thickness, we get:

    • δ = 5.0 x 0.25/√13,500 = 0.0028 m or 2.8 mm

  • The shear stress at the middle of the plate can be calculated using the formula:

    • τ_w = 0.664 x √(ρ x V x μ)

  • Putting the values, we get:

    • τ_w = 0.664 x √(900 x 6 x 0.0009) = 0.060 N/m^2

  • The average shear stress can be calculated using the formula:

    • τ_avg = Friction drag / A

  • Putting the values, we get:

    • τ_avg = 142.3 / 0.1 = 1423 N/m^2

  • The shear stress at the trailing edge can be assumed to be zero as the velocity gradient is zero at the boundary layer edge and the velocity at
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Calculate the friction drag on a plate 0.5 m × 0.2 m placed longitudinally in a stream of oil (specific gravity 0.9 and kinematic viscosity 1 stokes) flowing with a free stream velocity of 6 m/s. Also, calculate the boundary layer thickness and shear stress at the middle of the plate. Compare average shear stress with shear stress at the trailing edge.?
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Calculate the friction drag on a plate 0.5 m × 0.2 m placed longitudinally in a stream of oil (specific gravity 0.9 and kinematic viscosity 1 stokes) flowing with a free stream velocity of 6 m/s. Also, calculate the boundary layer thickness and shear stress at the middle of the plate. Compare average shear stress with shear stress at the trailing edge.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Calculate the friction drag on a plate 0.5 m × 0.2 m placed longitudinally in a stream of oil (specific gravity 0.9 and kinematic viscosity 1 stokes) flowing with a free stream velocity of 6 m/s. Also, calculate the boundary layer thickness and shear stress at the middle of the plate. Compare average shear stress with shear stress at the trailing edge.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the friction drag on a plate 0.5 m × 0.2 m placed longitudinally in a stream of oil (specific gravity 0.9 and kinematic viscosity 1 stokes) flowing with a free stream velocity of 6 m/s. Also, calculate the boundary layer thickness and shear stress at the middle of the plate. Compare average shear stress with shear stress at the trailing edge.?.
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