Using numerical results for the Blasius exact solution for laminar boundary-layer flow on a flat plate, (Section 9.2 on the web) plot the dimensionless velocity profile, u/U (on the abscissa), versus dimensionless distance from the surface, y/δ (on the ordinate). Compare with the approximate parabolic velocity profile of Problem 9.8.
9.8 Velocity profiles in laminar boundary layers often are approximated by the equations
Compare the shapes of these velocity profiles by plotting y/δ (on the ordinate) versus u/U (on the abscissa).
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
Statics and Mechanics of Materials (5th Edition)
Fundamentals Of Thermodynamics
Fundamentals of Heat and Mass Transfer
Engineering Mechanics: Dynamics (14th Edition)
DeGarmo's Materials and Processes in Manufacturing
Thinking Like an Engineer: An Active Learning Approach (3rd Edition)
- Question 11) Vortices are usually shed from the rear of a cylinder, which are placed in a uniform flow at low speeds. The vortices alternatively leave the top and the bottom of the cylinder, as shown in figure, causing an altemating force normal because of generating a dimensionless relationship for Kánmán vortex shedding frequency f (1/s) as a function of free-stream speed V(7m/s), fluid density p (kgm³), fluid viscosity µ (kg/m.s), sound velocity c (m/s), surface roughness & (m) and cylinder diameter D(m). || I-Determine the nondimensional a parameters using repeating variables, involving f, , c and u as nonrepeating variables ii-the dynamics of Bhosphorus bridge is investigated in a wind tunnel for the vortex generation behind the wires. A 1/59 scaled down model of the hanging wires is used in the laboratory. If vortex shedding frequency of of Bhosphorus bridge 590 Hz is measured in the laboratory at 29 m/s. Then detemine the expected frequency in the actual case exposed to 190 km/h…arrow_forwardA wind tunnel has a cross-section of 1.0m at its inlet by 1.0m and length 10m. Wind at uniform velocity 15m/s enters the tunnel at 20°C. Assume, velocity distribution in turbulent 1/5 y boundary layer to follow the law U (Kinematic viscosity= 1.53x10°m² /s) Assuming the boundary layer to be turbulent from the beginning, then the value of 8(represents in law) is calculated asarrow_forwardVortices are usually shed from the rear of a cylinder, which are placed in a uniform flow at low speeds. The vortices alternatively leave the top and the bottom of the cylinder, as shown in figure, causing an alternating force normal because of generating a dimensionless relationship for Kármán vortex shedding frequency fk (1/s) as a function of free-stream speed V(m/s), fluid density r (kg/m3), fluid viscosity µ (kg/m.s), sound velocity c (m/s), surface roughness ɛ (m) and cylinder diameter D(m). Solve the problem by making the necessary assumptions and drawing the schematic figure. I-Determine the nondimensional p parameters using repeating variables, involving f, ɛ, c and µ as nonrepeating variables ii-the dynamics of Bhosphorus bridge is investigated in a wind tunnel for the vortex generation behind the wires. A 1/56,2 scaled down model of the hanging wires is used in the laboratory. If vortex shedding frequency of of Bhosphorus bridge 562 Hz is measured in the laboratory at…arrow_forward
- From 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_forwardQ.1 The velocity distribution in a turbulent boundary layer is given by 1/7 %3D What is the displacement thickness 8*?arrow_forwardMeasuring in Boundary-layers flows on a flat plate for x= 0.265 and x= 0.115m Lab conditions are: Patm = 750 mm Hg T atm = 19 degrees C Manometer angle Beta = 60 degrees Could you please help me process this dataarrow_forward
- Consider fully developed two-dimensional Poiseuille flow—flow between two infinite parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dx driving the flow as illustrated in Fig. (dP/dx is constant and negative.) The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity components are given by u = 1/2? dP/dx (y2 − hy) ? = 0where ?isthefluid’sviscosity.Isthisflowrotationalorirrotational? If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise?arrow_forwardQ.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 x 105, maximum distance, from leading edge up to which the boundary layer remains laminar, isarrow_forwardIf a missile takes off vertically from sea level and leavesthe atmosphere, it has zero drag when it starts and zerodrag when it finishes. It follows that the drag must be amaximum somewhere in between. To simplify the analysis,assume a constant drag coefficient, CD, and constant verticalacceleration, a. Let the density variation be modeled by thetroposphere relation. Find an expression for thealtitude z* where the drag is a maximum. Comment onyour result.arrow_forward
- Mott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?arrow_forwardThe radius of the blood vessel is 0.9 cm with a viscosity and density of 0.004 kg/(m-sec) and 1010 kg/m^3. Find the Reynolds number if the flow velocity is 0.18 m/sec? 1018 918 618 718 818 Kinematic similarity is about similarity of ...arrow_forwardThe drag of a sonar transducer is to be predicted, based on wind (Air) tunnel test data. The prototype is 1.5 m diameter sphere, is to be towed at 4.3 m/s in seawater. The model is 0.2 m diameter. Take: Air density = 1.2 kg/m, Air dynamic viscosity = 1.81 x 10$ Pa. s, seawater density = 1000 kg/m, seawater dynamic viscosity 1.813x 10 Pa s, If the drag of the model at these test conditions is 9.5 N, estimate the drag of the prototype in (N).arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY