Water flows past a flat plate that has a length L = 5 m and a width w = 2 m, as shown in Figure Q4. The shear stress at the wall is given by Tw = μ du dy. When the flow is laminar the shear stress at the wall is given by the equation: Tw = 0.0644 pU∞ 2 6 x Where p = 1000 kg/m3 is the water density and U∞ = 5 m/s is the velocity of the water. The height of the boundary layer is d, and can be approximated by 8(x) = 5√ ux pU" The viscosity of water is μ = 1 mPa.s. a) Estimate the drag force on the plate. You may use the expression FD = | TwdA b) When the flow becomes turbulent, we can approximate the velocity gradient at the wall as constant, au ay = A. If the total drag force is 300 N, find A. c) When the fluid is heated to 900C, the density drops slightly and the viscosity decreases a lot, and engineers observe that the equation, Tw = 0.0644pU 2 5 x, becomes less accurate. Explain why this might occur (1-2 sentences). d) In order to visually examine a turbulent boundary layer, engineers release a steady stream of dye from the front of the plate. Does this represent (i) streamlines, (ii) streaklines, (iii) pathlines, (iv) all three.

Water flows past a flat plate that has a length L = 5 m and a width w = 2 m, as shown in Figure Q4. The shear stress at the wall is given by Tw = μ du dy. When the flow is laminar the shear stress at the wall is given by the equation: Tw = 0.0644 pU∞ 2 6 x Where p = 1000 kg/m3 is the water density and U∞ = 5 m/s is the velocity of the water. The height of the boundary layer is d, and can be approximated by 8(x) = 5√ ux pU" The viscosity of water is μ = 1 mPa.s. a) Estimate the drag force on the plate. You may use the expression FD = | TwdA b) When the flow becomes turbulent, we can approximate the velocity gradient at the wall as constant, au ay = A. If the total drag force is 300 N, find A. c) When the fluid is heated to 900C, the density drops slightly and the viscosity decreases a lot, and engineers observe that the equation, Tw = 0.0644pU 2 5 x, becomes less accurate. Explain why this might occur (1-2 sentences). d) In order to visually examine a turbulent boundary layer, engineers release a steady stream of dye from the front of the plate. Does this represent (i) streamlines, (ii) streaklines, (iii) pathlines, (iv) all three.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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