A cubic approximate velocity profile was used in Problem 5.12 to model flow in a laminar incompressible boundary layer on a flat plate. For this profile, obtain an expression for the x and y components of acceleration of a fluid particle in the boundary layer. Plot ax and ay at location x = 3ft, where δ = 0.04 in., for a flow with U = 20 ft/s. Find the maxima of ax at this x location.
5.12 A useful approximation for the x component of velocity in an incompressible laminar boundary layer is a cubic variation from u = 0 at the surface (y = 0) to the freestream velocity, U. at the edge of the boundary layer (y = δ). The equation for the profile is u/U =
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Fox and McDonald's Introduction to Fluid Mechanics
- is shown the unsteady-state streamlines of a cylinder moving with a uniform velocity U in the fluid at rest. Calculate and draw the un- steady-state streamlines at an interval of 10° (0 = 10°). The tangential com- ponent of velocity on the surface of the cylinder in a uniform stream, U., is given by r = -2U sin 0. UR31 URA URS URG I URI UR2 Us Uo U Cylinder moving with velocity U in fluid at rest (b) Streamlines, Unsteady Flowarrow_forwardIn chapter 12, we found the velocity profile for flow around a sphere using the creeping flow approximation. For the flow, derive the velocity profile for V, and Ve. Also, find the pressure distribution P. Finally, find the drag force acting on the sphere. (Hint: use the following integration ranges (1) 0<0<â and (2) 0<ô<2à). You can use all the assumptions that we made for this flow in the class.arrow_forwardFluid dynamicsarrow_forward
- If a body with a linear dimension of 1 ft is moving in a fluid with velocity q, find the Froude number and the Reynolds number for the follow- ing cases: (a) when the fluid is air and has 4 100 ft/sec; (b) when the 1 fluid is water and has q - 5 ft/sec.arrow_forwardPlease don't use Artificial intelligence tools. Only handwritten. Mechanical engineering (fluid mechanics)arrow_forwardfor a steady incomprssible two dimensional flow, represented in cartesian coordinates (x,y), a student correctly writes the equation of pathline of any arbitrary particle as dx/dt =ax and dy/dt= by where a and b are constants having unit of second‐¹. if value of a is 5 determine the value if b.arrow_forward
- for a steady incompresible two dimensional flow, represented in cartesian coordinates (x,y), a student correctly writes the equation of pathline of any arbitrary particle as dx/dt =ax and dy/dt= by where a and b are constants having unit of second‐¹. if value of a is 5 determine the value if b.arrow_forward3. Consider the laminar flow of an incompressible fluid over a flat plate at y = 0. (a) Assume the velocity profile of the boundary layer u is a sinusoidal function. Solve = fm), where U is the freestream velocity and 7 = y/5. (b) From momentum integral equation, express Cf, Tw in terms of Rex.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
- An equation for the velocity for a 2D planar converging nozzle is Uy u =U1+ w=0 L Where U is the speed of the flow entering into the nozzle, and L is the length. Determine if these satisfy the continuity equation. Write the Navier-Stokes equations in x and y directions, simplify them appropriately, and integrate to determine the pressure distribution P(x.y) in the nozzle. Assume that at x = 0, y = 0, the pressure is a known value, P.arrow_forwardProblem 1: Write the boundary conditions for the following flows: a) Flow between parallel plates (Fig. 1) without a pressure gradient. The upper plate is moving with velocity V. y = +h y = -h Fixed Fig. 1 V u(y)arrow_forwardthe flow of a stream U, past a blunt flat plate creates a broad low-velocity wake . , with only half of the flow shown due to symmetry. The velocity profile behind the plate is idealized as “dead air" (near-zero velocity) behind the plate, plus a higher velocity, decaying vertically above the wake according to the variation u = U, + AU e2, where L is the plate height and z = 0 is the top of the wake. Find AU as a function of stream speed Ug. behind the plate. A simple model is given in Fig. Uo Exponential curve Width b Uo into paper U+AU Dead air (negligible velocity) € -arrow_forward
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