Example 6. For free flow of air over a plate, it is given that Grashof number is 7 x 10° and Prandtl number is 0.25. Then, determine the type of flow.
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- [4] Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates. The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is he, and the gravity acts in the negative z-direction (in to the page). There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. Calculate the velocity and pressure fields, and estimate the shear force per unit area acting on the bottom plate. Moving plate Flui Finod plateFor free flow of air over a plate, it is given that Grashof number is 7 x 10º and Prandtl number is 0.25 Then, determine the type of flow.A 20degC water flows to 50cmx60cm flat plate with velocity of 3m/s . The flat plate surface temperature is maintained at 40deg 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? Round your answer to 2 decimal places.
- A potential steady and incompressible air flow on x-y plane has velocity in y-direction v= - 6 xy . Determine the velocity in x-direction u=? and Stream Function SF=? ( x2 : square of x ; x3: third power of x ; y2: square of y , y3: third power of y)ANSWER: u= 3 x2 - 3 y2 SF= 3 x2 y - y3If a vertical wall at temperature T, is surrounded by a fluid at temperature T, a natural convection boundary layer flow will form. For laminar flow, the momentum equation is au ди. p(u-+ v) = PB(T – T)g + µ- ди ay to be solved, along with continuity and energy, for (u, v, T) with appropriate boundary conditions. The quantity B is the thermal expansion coefficient of the fluid. Use p, g, L, and (Tw- To) to nondimensionalize this equation. Note that there is no “stream" velocity in this type of flow.Air flows over a stationary flat plate at speed of 4,6 m/s . Plate has a width of 1 m. Air has a density of 1.2 kg/m3 and kinematic viscosity of 1.5x 10-5 m 2/s . Consider plate is totally in air flow field and upper and lower surfaces are identical a) Calculate maximum length of the plate to have a fully laminar flow (in m) b) Calculate total frictional force on the plate considering two surfaces (in N) c) In order to eliminate the frictional force on its surfaces calculate the plate speed(in m/s)
- Velocity profile inside boundary layer is given as, U sin 2 8 U. Find the value ofTwo endlessly long flat plates, separated by 3 inches in distance but with a thickness of 5 inches, each transport alcohol (5 m/s, 1 Pa·s, S.G. 0.89 (ref. water at 4 degrees Celsius) to a given location with a specific velocity. Prove that the Reynold's number of the following problem is a value approximately around 90-100.Perform the convective on velocity vectors u in cylindrical coordinates : Du/Dt
- 1.what Reynolds number let Fluid properties in pipe flow are Laminar and Turbulent flow 2. what Reynolds number let Boundary Layer are Laminar and Turbulent flowWe are testing a flat plate of length L = 1.125 m and width W = 0.225 m in a stream of air flowing with a velocity of 20 m/s. In test case 1, the air is flowing parallel to L and in test case 2 air is flowing parallel to W. Find: What portion of the boundary layer flow is laminar in each case? What is the highest laminar boundary layer thickness in each case? Assuming the flow is entirely turbulent over the plate, calculate the drag force in both test cases Take air density as 1.2 kg/m3 and its viscosity as μ=18×10−6μ=18×10−6 N.s/m2.Air flows over a stationary flat plate at speed of 4,3 m/s. Plate has a width of 1 m. Air has a density of 1.2 kg/m³ and kinematic viscosity of 1.5x 105 m²/s. Consider plate is totally in air flow field and upper and lower surfaces are identical a) Calculate maximum length of the plate to have a fully laminar flow (in m) Yanıt: b) Calculate total frictional force on the plate considering two surfaces (in N) Yanıt: c) In order to eliminate the frictional force on its surfaces calculate the plate speed (in m/s) Yanıt: