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A horizontal flow initially at Mach I flows over a downward-sloping expansion corner, thus creating a centered Prandtl-Meyer expansion wave. The streamlines that enter the head of the expansion wave curve smoothly and continuously downward through the expansion fan, and emerge parallel to the downward sloping surface downstream of the tail of the wave, as shown in Figure 9.2b. Imagine a polar coordinate system
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Fundamentals of Aerodynamics
- Problem9 The entrance flow between two parallel plates (gap h) has a velocity that varies linearly at the entrance and develops into a fully parabolic profile at the exit. What is the relationship between the maximum velocity at the entrance and that at the exit? You can show by symmetry that the maximum velocity is attained at the mid-plane between the two plates.arrow_forwardQuestion 5. Consider a plane source of strength A = 121 m²/s at(-a, 0), and a plane sink of equal strength at (a, 0) where a = 1m, and superpose a uniform stream of V,= 45m/s with 22° angle of attack with respect to x axis. (a) Find the coordinate of the stagnation point(s). (b) Find the streamline passing through the stagnation points. (c) What is the geometric definition of the body generated by this superposition? Plot the body. (d) What is the maximum velocity and C, on this body? (e) Plot the streamlines for this flow.arrow_forward3. A simple flow model for a two-dimensional converging nozzle is the distribution U,(1+ v = -U, L w = 0 Determine equation for the streamlines.arrow_forward
- A. A horizontal water jet hits a vertically mounted plate and an obliquely mounted plate as shown in Fig 2 (a) and (b), respectively. The jet is assumed to have the (a) uniform velocity distribution of V and the density of the fluid is p. The volume flow rate is Q. The effect of viscosity is assumed to be negligible. Answer the following questions. ►Fa V (1) In the case of (a), obtain the force exerted on the vertical plate Fa using p, Q and V.arrow_forwardA horizontal jet, with a density of 1097 kg/m and a diameter of 14.6 cm, is deflected upwards by a 90° bend. Calculate the force needed to keep the bend in place. The inflow has a uniform velocity v₁ = (1.8; 0; 0) m/s, and ambient pressure is 1.18 bar. The flow is non-viscous, the water jet leaves with a diameter of 10.4 cm, and the mass of the bend itself may be neglected. Both in- and outflow have a circular cross-section. Give your answer in 1 decimal accuracy. Y L. FI == sn N Fy = ___ N -arrow_forwardProblem6 When a viscous fluid flows parallel to a horizontal plate, it leads to the development of a thin boundary layer on the plate surface. The velocity within the boundary layer varies with the vertical direction as u(y) = U∞ where 8(x) = 3.5 X is the boundary layer thickness ¯ 8(x) / that increases with the horizontal position. Outside of the boundary layer, the flow is uniform and equal to the free stream velocity U... Show that for two fluids of different viscosities (₁, ₂) and densities (P₁, P₂) and flowing at the same free stream velocity, the ratio of the drag force they generate on the plate is proportional to the square root of the ratio of the viscosities and densities: FD2 FD1 = H₂P2 H1P1arrow_forward
- A jet of water of 75 mm diameter moving with a velocity of 15 m/s impinges on a fixed plate. Find the force exerted on the plate in the direction of the jet. when the angle between the plate and the jet is 25°. [Ans. 177.5 N]arrow_forwardA point source with volume flow Q = 30 m3/s is immersedin a uniform stream of speed 4 m/s. A Rankine half-body ofrevolution results. Compute (a) the distance from the source to the stagnation point and (b) the two points (r, θ) on thebody surface where the local velocity equals 4.5 m/s.arrow_forwardThe converging-diverging flow domain is shown in Figure 1. The inlet diameter is 0.2 m, the throat diameter is 0.15 m, and the outlet diameter is 0.24 m. The axial distance from the inlet to the throat is 0.30 m—the same as the axial distance from the throat to the outlet. At the inlet section, the stagnation pressure P0 is set to 220 kPa (absolute), while the stagnation temperature T0, at the inlet is set to 300 K.arrow_forward
- A jet of water of 100 mm diameter is striking a plate with a velocity of 35 m/s. Find the force exerted by the jet in a direction normal to the plate. if the plate is inclined at 30° with the jet. [Ans. 4.81 kN]arrow_forwardA group of students is designing a small, round (axisymmetric), low-speed wind tunnel for their senior design project. Their design calls for the axial component of velocity to increase linearly in the contraction section from uz, 0 to uz, L. The air speed through the test section is to be uz, L = 120 ft/s. The length of the contraction is L = 3.0 ft, and the entrance and exit diameters of the contraction are D0 = 5.0 ft and DL = 1.5 ft, respectively. The air is at standard temperature and pressure. (a) Verify that the flow can be approximated as incompressible. (b) Generate an expression for the radial velocity component ur between z = 0 and z = L, staying in variable form. You may ignore frictional effects (boundary layers) on the walls. (c) Generate an expression for the stream function ? as a function of r and z. (d) Plot some streamlines and design the shape of the contraction, assuming that frictional effects along the walls of the wind tunnel contraction are negligible.arrow_forwardThe flow past a two-dimensional Half-Rankine Body results from the superposition of a horizontal uniform flow of magnitude U= 3 m/s towards the right and a source of strength g = 10 m2/s located at the origin (0, 0). The fluid density is 1000 kg/m³. All dimensional quantities are given in SI units. Neglect the effects of gravity. The x-coordinate of the stagnation point is x = m. The total width of the body is 2. m. The magnitude of the pressure difference between the points (-1, 0) and (0, 2) is kPa. Enter the correct answer below. Please enter a number for this text box. 2 Please enter a number for this text box. Please enter a number for this text box.arrow_forward
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