Table 9.1 (on the web) shows the numerical results obtained from Blasius exact solution of the laminar boundary-layer equations. Plot the velocity distribution. On the same graph, plot the turbulent velocity distribution given by the
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Additional Engineering Textbook Solutions
Engineering Mechanics: Statics
Statics and Mechanics of Materials (5th Edition)
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Mechanics of Materials
Engineering Mechanics: Statics & Dynamics (14th Edition)
Mechanics of Materials (10th Edition)
- In the flow of air at 20°C and 1 atm past a flat plate inFig. , the wall shear is to be determined at position x bya floating element (a small area connected to a strain-gageforce measurement). At x = 2 m, the element indicates ashear stress of 2.1 Pa. Assuming turbulent flow from the leadingedge, estimate (a) the stream velocity U, (b) the boundarylayer thickness δ at the element, and (c) the boundary layervelocity u, in m/s, at 5 mm above the element.arrow_forwardConsider two pressure taps along the wall of a laminar boundary layer as in Fig. The fluid is air at 25°C, U1 = 13.7 m/s, and the static pressure P1 is 2.96 Pa greater than static pressure P2, as measured by a very sensitive differential pressure transducer. Is outer flow velocity U2 greater than, equal to, or less than outer flow velocity U1? Explain. Estimate U2arrow_forwardThis is a practice question, not graded assignment. Understand that to find the answer to below question, we need to solve Navier-Stokes and energy equation for this flow to derive the velocity profile and temperature profile. Please show step-by-step equations including step-by-step integration. Please also provide explanation. An incompressible fluid flows through a rectangular cross section duct, with width much larger than height of the cross section. The duct surface is heated at a uniform rate along its length. If the centreline of the flow is along the centre of the duct where y = 0, the distance from the centreline to the surface of the duct is b = 25 mm, and the thermal conductivity of the fluid is 0.6 W/mK, what is the local heat transfer coefficient in the developed region of the flow? Give your answer in W/m^2K to 1 decimal place.arrow_forward
- Using von Karman momentum integral, derive boundary layer height 8, boundary layer displacement thickness d, boundary layer momentum thickness 0, wall shear stress To, local skin friction coefficient c, and total drag coefficient C, for turbulent boundary layer flow with power law constant, n = 5. Discuss by comparing your answers to turbulent boundary layer flow with power law constant, n = 7. Take the empirical wall shear stress: To = 0.0204pU 2 %3D SU 1/4arrow_forwarde. b. C. d. a. EME3026 Question 2 A dimensionless velocity profile, u* = u/U = Co + C₁-C₂y, where, y = y/8, is proposed to approximate the laminar boundary layer solution for flow around a corner. The outer flow velocity can be expressed as, U = C²x, where, C, is constant. Boundary layer has the thickness of, 8, where, Co. C₁, and C₂, are the constants to be determined in order to match the boundary conditions in the boundary layer, including the no slip condition, match the outer flow velocity and zero shear stress at the edge of the boundary layer. Apart from that, an additional boundary condition is proposed. a²u dyz y=0 Given the fluid kinematic viscosity, v = 1.46 x 10-5 m²/s and the constant, C² = 0.09 s-¹. Validate the proposed additional boundary condition. FLUID DYNAMICS U (dU Find the velocity profile, u", by evaluating the constant, Co, C₁, and C₂. = --- Determine the displacement thickness and momentum thickness in term of boundary layer thickness. Show that the general…arrow_forwardThe momentum thickness OM for laminar flow over a flat plate is (115/1134) 6. Find the following: a) Boundary layer thickness (6) divided by x. Compare this answer to the Blasius Solution. Answer should be 6/x = 5.733/sqrt(Rex). b) Local skin friction coefficient (cf). Answer hould be 0.5814/sqrt(Rex). c) Friction Drag Coefficient. Answer should be 1.1628/sqrt(Rex).arrow_forward
- Help me pleasearrow_forwardA liquid flows tangentially past a flat plate. Given: u=10 Ns/m², p=1.5kg/m', L= 2m,approach velocity U = 20 m/s. The %3D boundary layer thickness is equal to a. 8 = 0.34 cm b. 8 = 3.4 cm С. 8 = 0.034 cm %3D d. 8 = 34 cmarrow_forward3. Pressure Flow, Flat Plates. Adverse pressure gradients in flow over bodies lead to flow reversal & separation, wakes, and increased drag. To examine such behavior, consider fully developed, laminar flow between two flat pates a distance 8 apart. The bottom plate is fixed, and the top plate moves with speed U (representing the outer flow over a boundary layer of thickness 8). (a) Derive the critical adverse pressure gradient, (dp/dx)*, above which there will be flow reversal, by solving the N-S equation in the coordinates shown, to get a relation for u(y), du/dy, and the critical (dp/dx)* in terms of 8, U, and u above which there μ will be flow reversal at the lower plate. (b) If 8 = 5 mm and U = 10 m/s, evaluate (dp/dx)* if the fluid is air. Moving plate Fixed plate 2/ 1.0 0.8 0.6 0.4 0.2 Back- flow P=-3 0 -0.4 -0.2 0 0.2 0.4 u U (b) U 0.6 0.8 1.0 1.2 b 1.4 (a) FIGURE 6.30 Viscous flow between parallel plates with the bottom plate fixed and the upper plate moving (Couette flow): (a)…arrow_forward
- Q.3 Air (density 1.2 kg/m3 and kinematic viscosity 15 centistokes) flows over a flat plate, at zero angle of incidence, at a velocity of 20 m/s. If Reynolds number at transition is taken as 2.5 × 105, maximum distance, from leading edge up to which the boundary layer remains laminar isarrow_forwardFrom the laminar boundary layer the velocity distributions given below, find the momentum thickness θ, boundary layer thickness δ, wall shear stress τw, skin friction coefficient Cf , and displacement thickness δ*1. A linear profile, u(x, y) = a + by 2. von K ́arm ́an’s second-order, parabolic profile,u(x, y) = a + by + cy2 3. A third-order, cubic function,u(x, y) = a + by + cy2+ dy3 4. Pohlhausen’s fourth-order, quartic profile,u(x, y) = a + by + cy2+ dy3+ ey4 5. A sinusoidal profile,u = U sin (π/2*y/δ)arrow_forwardEstimate the drag force on the fuselage shown below for a cruising speed of 210 m/s at 10,000m. Hint 1: To calculate the drag force split the fuselage into 4 parts: front hemisphere,cylindrical body, vertical stabilizer, back hemisphere. Model the front and back hemispheres as flow over a sphere. For simplicity treat the cylindrical body and vertical stabilizer as flat plates.Hint 2: Use Cd vs Reynolds number graphs for sphere and flat plate. If your Reynolds number is greater/smaller than the Cd vs Reynolds graph range, you can instead use the greatest/smallest number available on the graph.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning