Consider the boundary layer growing on a flat plate aligned at the freestream flow, Plot local skin frietion coefficient
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Fluid Mechanics: Fundamentals and Applications
- When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the weight of the sphere is balanced by the buoyant force and the frictional resistance of the fluid. Make a dimensional analysis of this problem and indicate how experimental data for this problem could be correlated. Neglect compressibility effects and the influence of surface roughness.arrow_forwardFor the flow geometry from the top of a flat plate, the velocity profile around the plate is given as v (y) = ay+by^2-cy^3, and the temperature profile as T (y) = d+ey+fy^2-gy^3. Derive the mathematical expressions that give the regression coefficient and the heat transfer coefficient. CREATE THE KNOWN AND UNKNOWN BY DRAWING THE SHAPE OF THE ORGANIZATION AND WRITE ALL THE ASSUMPTIONS IN DETAILarrow_forward9:25 G令. View Recordings PROBLEM SET A (4 problems) Problem 1 The sliding plate viscometer shown below is used to mensture the viscosity of a fluid. The top plate is movmg to the right with a coustant velocity of 10 m's in re stationary. What is the viscosity of the fluid? Assume a linear velocity distribution e to a force of 3 N. The bottom plate is to m 1 mm Problem 2 Calculate the density and specific weight of carbou dioxide at a pressure of 300 kN'm“ absolute and 60°C. Problem 3 A 10 m' oxygen tank is at 15°C and 800 kPa. The valve is opened, and some oxygen is released until the pressure in the tank drops to 600 kPa. Calculate the mass of oxygen that has been released from the tank if the temperature in the tank does not change during the process. 40:45 59:06 C ||arrow_forward
- In the field of air pollution control, one often needs to sample the quality of a moving airstream. In such measurements a sampling probe is aligned with the flow as sketched in Fig. A suction pump draws air through the probe at volume flow rate V· as sketched. For accurate sampling, the air speed through the probe should be the same as that of the airstream (isokinetic sampling). However, if the applied suction is too large, as sketched in Fig, the air speed through the probe is greater than that of the airstream (super iso kinetic sampling). For simplicity consider a two-dimensional case in which the sampling probe height is h = 4.58 mm and its width is W = 39.5 mm. The values of the stream function corresponding to the lower and upper dividing streamlines are ?l = 0.093 m2/s and ?u = 0.150 m2/s, respectively. Calculate the volume flow rate through the probe (in units of m3/s) and the average speed of the air sucked through the probe.arrow_forward(b) In two dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = ở. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. C5 Table 2: Equation of Velocity Profile Setting Equation wU = 2y/8 - (y/S² 1arrow_forward9 of the diffusion Term of The The Expression below is part Nallier-Stokes equation in spherical coordinates. what are units of this term I given it is dynamic viscosity [Pa-s] T A partial derivative behave the same as a full devevarive. 2 дио r² sin(0) do unit ? Expression: anshuar: T ris position, is velosity: A does not have dimension Mf-arrow_forward
- A small low-speed wind tunnel is designed to calibrate hot wires (anemometer wires) (Figure 2). The air temperature is 19 OC. The test section of the wind tunnel is 30 cm in diameter and 30 cm in height. The flow through the test section must be as uniform as possible. The speed range of the wind tunnel varies from 1 M/s to 8 M/S, and the design will be optimized with an airspeed of V= 4.0 M / s in the test section. For a flow state at a speed of 4.0 m/S, which is almost uniform at the entrance to the test section, how fast does the air velocity on the tunnel axis accelerate to the end of the test section?Note: kinematic viscosity of air at 19 C ν=1. 507x10-5 m2 / sarrow_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_forwardMott ." 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_forward
- 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_forward1. A fluid is bounded by two parallel plates of infinite width and length as shown in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is fixed. The fluid's dynamic viscosity is 1.85X105 N.s/m?. Assume Couette flow with pressure gradient, = 0.1 N/m³. a. Propose the discretization method to solve Couette flow equation with pressure gradient below. Let the number of nodes, n = 9, the distance between the nodes is 0.05 m. Obtain the velocity of all the internal nodes using the matrix inversion method and the iterative method. Compare the results and the effectiveness of both methods (in terms of calculation effort and ease of setting up the problem). + b. Flow shear stress is governed by the following equation ôu Propose the discretization method to solve the above equation and calculate the shear stress at node 1. Describe the condition in tems of the pressure gradient when the shear stress at the bottom plate is zero. Moving plate at Um/s N= N-1 `Fixed plate FIGURE Q1arrow_forwardReference 12 contains inviscid theory calculations for the upper and lower surface velocity distributions V(x) over an airfoil, where x is the chordwise coordinate. A typical re- sult for small angle of attack is as follows: xlc VIU„(upper) VIU„(lower) 0.0 0.0 0.0 0.025 0.97 0.82 0.05 1.23 0.98 0.1 1.28 1.05 1.13 0.2 1.29 0.3 1.29 1.16 0.4 1.24 1.16 0.6 1.14 1.08 0.8 0.99 0.95 1.0 0.82 0.82 Use these data, plus Bernoulli's equation, to estimate (a) the lift coefficient and (b) the angle of attack if the airfoil is symmetric.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning