Assume the critical Reynolds number for the flow to be considered as laminar over a flat plate is 5 × 105. Determine the distance from the leading edge at which transition will occur for atmospheric air when u∞ = 1 m/s and T∞ = 27 °C. Use T∞ to find relevant properties in Table A.4.
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- A square block is weighing 300 N and having a length of 20 cm on one edge slips on a 20° inclined surface in which there is a film of SAE 30 at 10°C oil. What is the terminal velocity of the block down the incline if the oil thickness at this condition is 1 mm?Consider an airflow over the surface of a flat plate with a temperature Ts = 250 °C. At some distance from y the origin, the temperature profile of the airflow is given by the following function: q/A As, Ts T(y) = T, -(T. -T3)exp -u. y a fluido dAs The airflow at atmospheric pressure has a free flow velocity u.. = 0.06 m/s and a temperature T = 15°C. The thermal diffusivity of the fluid is aluid = 3.872E-05 m?/s and its thermal conductivity Afluid = 0.03383 W/(m K). 1. Determine the heat flux over the surface of the plate. q/A = W/m? 2. Determine the convection coefficient of the airflow. h = W/(m² K)Cooling water for a power plant is stored in a pond 900 m in length and 400 m wide. A dry wind at 300 K blows in a horizontal direction parallel to the 900 m side of the pond at a velocity of 2 m/s. The cooling water is at 300 K. Known the air dynamic viscosity v= 1.67 x10m?/s.; the Re transition from laminar flow to turbulent flow is 500,000; and the saturated water vapor pressure at 300 K is 3580 Pa; gas constant R= 8.3144 J/mole.K. 1.) At what position across the pond is the air flow no longer laminar? Would it reasonable to assume that the mean gas-film mass transfer coefficient for water vapor in air is dominated by turbulent flow mass transfer? 2.) As part of an engineering analysis to predict the evaporation rate of water from the pond, determine the mean gas film mass transfer co-efficient. 3.) Calculate the rate of water evaporation from the pond.
- Engine oil at 100°C flows on the top surface of a 1-m-long flat plate maintained at 20°C. The oil’s freestream speed (u infinity) is 0.1 m/s. Find the engine oil properties from the table A.5 A. Evaluate the Reynolds number, local convection coefficient, heat flux and shear stress at the end of the plate (x = L). Is the air flow laminar or turbulent over the plate?B. Evaluate the average convection coefficient, average heat flux, average shear stress and drag force over the plate.Given engine oil at 60 oC flows over the upper surface of a 5 m long flat plate which temperature is 20 oC. Justify the value of x (m2/s) to get the turbulent flow for the total drag force and the rate of heat transfer per unit width of the plate. Discuss your idea.Consider laminar flow entering a tube. Before the fluid enters, the velocity profile is constant and equal to to. The tube diameter is D and radius R. You are interested in estimating how much distance the fluid must travel into the tube before the classic Poiseuille parabolic velocity profile is established - this distance is called the "entrance length" or Zent- Using boundary layer theory, which of the following would be a reasonable estimate? (Hint: assume as flow enters the tube, you can model the growing viscous boundary layer as laminar flow over a flat plate, and note that the De where v = Reynolds number for a tube is Rep %3D Zent = (Rep) Zent = D 2 (Rep) Zent = 2. Rep - Rep O Zent R-Rep %3D O None of the above.
- 4. Consider fully developed laminar flow in the annular space formed by two concentric cylinders with a pressure gradient, op/ax, and the inner cylinder stationary. Let r = Rand r = kR. Assuming that the velocity profile is given by u: [¹-( 7 )² + +(ma 1 R R² ap 4μ &x 1-k² In- In(1/k) R a) Obtain an expression for the location of the maximum velocity as a function of k. b) Compare the limiting case, k→ 0,with the corresponding expression for flow in a circular pipe. c) Determine the volume flow rate. d) Find an expression for the average velocity. e) Compare the limiting cases for the volume flow rate and average velocity, k →0, with the corresponding expression for flow in a circular pipe.An approximation for the boundary-layer shape in is the formula u(y) - U sin 0 sys d where U is the stream velocity far from the wall and d is the boundary layer thickness, as in Fig. If the fluid is helium at 20°C and 1 atm, and if U = 10.8 m/s and 8= 3 cm, use the formula to (a) estimate the wall shear stress Tw in Pa, and (b) find the position in the boundary layer where t is one-half of Tw. -- y = 6 u(y)Air at standard pressure flows across a flat plate at 3m/s. The temperature surface is 50oC and the surrounding temperature is 20o Consider a point 1m away from the leading edge of the plate. See Table A-15 in Appendix 1 for properties of air. Find the local Nusselt number. Based on this Nusselt number, what is the local convective heat flux from the plate to the air?
- What is the critical value of the pressure coefficient for an airplane flying at 170m/s in air at 2 deg C?A 20 °C water flows to 50cmx60cm flat plate with velocity of 6m/s . The flat plate surface temperature is maintained at 40 °C . The air flows parallel to the 50cm side of the plate. If the kinematic viscosity of water is 78x10-8 m2/s, at what length the flow become turbulent? If the average laminar heat transfer coefficient of water is 7740W/m2 °C , what is the overall heat transfer at the laminar section?Q4 : Air is flowing over a long flat plat velocity 8 m/s . Determine the distance from the leading edge of the plate where the flow become turbulente , and the thickness of the boundary layer at that location . Take the properties for air: k = 0,02735 W/m.°C , v= 1.798 × 10°m²/s , Pr = 0.7228