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du 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- When the flow is laminar the shear stress at the wall is given by the equation: dy 8 Tw= 0.0644 pU²- 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 8, and can be approximated by 8(x) = 5 μx pU ∞ The viscosity of water is μ = 1 mPa.s. a) Estimate the drag force on the plate. You may use the expression FD = StwdA b) When the flow becomes turbulent, we can approximate the velocity gradient at the A. If the total drag force is 300 N, find A. ди wall as constant, = ду L c) When the fluid is heated to 90°C, the density drops slightly and the viscosity decreases a lot, and engineers observe that the equation, T₁ = 0.0644pU², 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. 18(x) Figure 04: Flow over a long flat plate. The boundary laver is shown by the light grey.

du 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- When the flow is laminar the shear stress at the wall is given by the equation: dy 8 Tw= 0.0644 pU²- 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 8, and can be approximated by 8(x) = 5 μx pU ∞ The viscosity of water is μ = 1 mPa.s. a) Estimate the drag force on the plate. You may use the expression FD = StwdA b) When the flow becomes turbulent, we can approximate the velocity gradient at the A. If the total drag force is 300 N, find A. ди wall as constant, = ду L c) When the fluid is heated to 90°C, the density drops slightly and the viscosity decreases a lot, and engineers observe that the equation, T₁ = 0.0644pU², 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. 18(x) Figure 04: Flow over a long flat plate. The boundary laver is shown by the light grey.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Question 4 du 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 When the flow is laminar the shear stress at the wall is given by the equation: dy Tw = 0.0644 PU ². 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 8, and can be approximated by 8(x) = 5 μx pU.. The viscosity of water is μ = 1 mPa.s. a) Estimate the drag force on the plate. You may use the expression F₁ = S twdA b) When the flow becomes turbulent, we can approximate the velocity gradient at the wall as constant, A. If the total drag force is 300 N, find A. du = ду c) When the fluid is heated to 90°C, the density drops slightly and the viscosity decreases a lot, and engineers observe that the equation, Tw 0.0644pU/ 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. 18(x) Figure 04: Flow over a long flat plate. The boundary layer is shown by the light grey.
Transcribed Image Text:Question 4 du 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 When the flow is laminar the shear stress at the wall is given by the equation: dy Tw = 0.0644 PU ². 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 8, and can be approximated by 8(x) = 5 μx pU.. The viscosity of water is μ = 1 mPa.s. a) Estimate the drag force on the plate. You may use the expression F₁ = S twdA b) When the flow becomes turbulent, we can approximate the velocity gradient at the wall as constant, A. If the total drag force is 300 N, find A. du = ду c) When the fluid is heated to 90°C, the density drops slightly and the viscosity decreases a lot, and engineers observe that the equation, Tw 0.0644pU/ 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. 18(x) Figure 04: Flow over a long flat plate. The boundary layer is shown by the light grey.
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