A fluid (v = 10-4 m²/s, p = 916 kg/m³) flows over a constant width, flat plate. The free- stream velocity is 4 m/s. Done What is the nature of the boundary layer (laminar/turbulent) 4 m downstream of the leading edge? Done What is the thickness, & of the boundary layer and the wall-shear stress, Tw at this location? Done →What is the velocity at a point 15 mm away from the plate at this location? d. What is the ratio of the shearing force on the upstream half of the plate to that on the ?? downstream half. Hint: Can you find out the shearing force on the upstream and downstream halves using the relations you have? Refer to the Blasius solution in the table below, and interpolate as needed. 25 T = May y[U/(vx)]¹/2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 u/U 0.0 0.06641 0.13277 0.19894 0.26471 0.32979 0.39378 0.45627 0.51676 0.57477 0.62977 0.68132 0.72899 0.77246 y[U/(vx)]¹/2 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 8 u/U 0.81152 0.84605 0.87609 0.90177 0.92333 0.94112 0.95552 0.96696 0.97587 0.98269 0.98779 0.99155 1.00000

Question 4: (10) Marks a) What is boundary layer separation? What are forces acting on it and effect of pressure gradient in the direction of flow? b) What are methods of controlling separation of boundary layer?

Question A3 a) With the help of sketches briefly describe the main differences between laminar and turbulent boundary layers in relation to friction drag and flow separation. A tug boat is pulling a log raft (Figure QA3) on the surface of a lake at a constant speed of Uboat = 5m/s. The log raft can be modelled as a flat plate (L=20m and W = 5.0m). u ug U boat 8 U Tug Boat rope boat Air Water L -X Log Raft Figure QA3 Assume the boundary layer forming on both sides (air side and water side) of the log raft is two-dimensional and laminar with a second order velocity distribution: W b) By using the Momentum Integral Equation find an expression for the wall shear stress in terms of Reynolds number and then estimate the tensile stress acting on the rope assuming the rope has a circular cross section with a diameter of 15 mm) and the power required to pull it. c) What would be the tensile stress on the rope if we assume the boundary layers on the log raft were turbulent? You may assume:…

Calculate the heat transfer from a 60 cm x 60 cm plate on which air flows at 40⁰C and. The plate temperature is 100⁰ C while the air speed is 5 m/s.Find the thickness of the boundary layer at a distance of x = 20 cm, for the same data in problem "number 1 In the picture below"