2. In a particular application involving airflow over a heated surface, the boundary layer temperature distribution may be approximated as T − Ts T∞ — Ts - = 1 – exp (−Pr- uooy ט 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 u∞/v = 5000 m²¹, what is the surface heat flux?
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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 hereMott ." 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?
- Please solve correctly and don't copy and paste chegg answers and solve by handFluid mechanicsThe 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
- The heat flux for stable film boiling on the outside of a horizontal cylinder or sphere of diameter D, in m, is given below. What should be the value of "n", for the equation above to be dimensionally consistent? Use dimensional analysis: q=heat flux, W m² W k = thermal conductivity of vapor, 'm °C hgf - [g kỷ Pv(P₁ − Pv)[hfg + 0.4 Cpv (Ts − Tsat)]] à = Cf MyD (Ts - Tsat) Pv = density of vapor, P₁ = density of liquid,- kg m³ kg 'm³ Cpv = enthalpy of vaporization, kg g = gravitatioinal acceleration, C = experimental constant, dimensionless m J kg °C Ts = surface temperature of the heater, °C Tsat = saturation temperature of vapor, °C kg Hv = viscosity of vapor, ms = specific hear of vapor, (Ts - Tsat)A- Womersley number (a) of a human aorta is 20 and for the rabbit aorta is 17, the blood density is approximately the same across the species. The values of viscosity were 0.0035 Ns/m² for the human and 0.0040 Ns/m² for the rabbit. The diameter of the aorta is 2.0 cm for the man, and 0.7 cm for the rabbit, estimate the heart rate beats per minute (bpm) for both speciesHi please show calculations or diagrams if required thank you
- 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…1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?Please help me to answer number (a) with detailed explanation by today. thank you