2. In a particular application involving airflow over a heated surface, the boundary layer temperature distribution may be approximated as T-Ts Top - Ts U∞oy. - = 1 − exp (−Pro v where y is the distance normal to the surface and the Prandtl number, Сри Pr = 0.7 k is a dimensionless fluid property. If T∞= 400 K, Ts= 300 K, and ux/v = 5000 m²¹, what is the surface heat flux? Answer: -9205W/m²
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- 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.Dimensional analysis concept applied hereThe Colburn equation for heat transfer is: 2/3 0.023 0.2 DG F';u is viscosity, lb h ft; k is thermal conductivity, where C, is heat capacity, Btu lb Btu h ft2 (°F ft); D is pipe diameter, ft; and G is mass velocity per unit area, lb h' ft. The Colburn equation is dimensionally consistent. What are the units and dimensions of the heat transfer coefficient, h?- -1
- 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?Fluid mechanicsA rectangular block of height Land horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below. Fluid 1 Pi(g/em³) Fluid 2 Block P:(g/cm³) Po(g/cm³) (a) Derive a formula for the block density, Pp, in terms of the fluid densities p, and p2, the heights họ. h1, and h2, and the cross-sectional area A. (It is not necessary that all of these variables appear in the final result.) (b) Force balances on the block can be calculated in two ways: (i) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (ii) in terms of the weight of the block and the buoyant force on the block as expressed by Archimedes' principle. Prove that these two approaches are equivalent.
- 2.0 m 7: 10.0 m = 2²-²² Us B 10.0 m Figure Q1-2 Question 2 Air flow at a constant speed (Us = 10 m/s) is forming a two-dimensional incompressible laminar boundary layer along a flat plate The velocity profile inside the boundary layer is given by: 2.0 m (Equation 1) At x = 1.00 m, the boundary layer thickness is given as 6.6094 mm. At this location: a) Determine the shear stress at the wall, at y = 3 mm and y = 10 mm. b) Calculate the boundary layer displacement thickness. c) Calculate the mass flow rate through the boundary layer per unit width. d) Calculate the mass flow rate per unit width of an ideal flow going through the same height as the boundary layer thickness. e) Through calculation relate the difference between the mass flow rates in parts (c) and (d) to the local boundary layer displacement thickness. In not more than 60 word justify your answer. Use sketch(s) to illustrate your justification. f) Does the assumed velocity profile satisfy the pressure boundary condition? In…PravinbhaiThe drag force on a submarine, which is moving on the surface, is to be determined by a test on a model which is scaled down to one-twentieth of the prototype. The test is to be carried in a towing tank, where the model submarine is moved along a channel of liquid. The density and the kinematic viscosity of the seawater are 1010 kg/m³ and 1.3x10-6 m 2/s, respectively. The speed of the prototype is 2.6 m/s. Assume that F = f(V, L. g. p.), using pi-theorem and similarity principle to: a) Determine the speed at which the model should be moved in the towing tank. b) Determine the kinematic viscosity of the liquid that should be used in the towing tank.
- Please help me to answer number (a) with detailed explanation by today. thank youAn incompressible Newtonian liquid is confined between two concentric circular cylinders of infinite length— a solid inner cylinder of radius Ri and a hollow, stationary outer cylinder of radius Ro. The inner cylinder be stationary and the outer cylinder rotate at angular velocity ?o. Generate an exact solution for u?(r) using the step-by-step . The flow is steady, laminar, and two-dimensional in the r?-plane. The flow is also rotationally symmetric, meaning that nothing is a function of coordinate ? (u? and P are functions of radius r only). The flow is also circular, meaning that velocity component ur = 0 everywhere. Generate an exact expression for velocity component u? as a function of radius r and the other parameters in the problem. You may ignore gravity.Please help me to answer question (B) by today with explanation. thank you