From Fourrier's law, the rate of heat transfer in plane surfaces is described by: Q = /(k, A, AT, x) where k = thermal conductivity (Watts/m-"C) Q = rate of heat transfer (Watts) A= area of the surface T= temperature difference x = thickness of the material If we are going to use Buckingham's Pi Theorem to determine dimensionless parameters, give possible combinations of repeating variables.
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- The drag on an airplane wing in flight is known to be a function of the density of air (), the viscosity of air(), the free-stream velocity (U), a characteristic dimension of the wing (s), and the shear stress on the surface of the wing (s). Show that the dimensionless drag, sU2, can be expressed as a function of the Reynolds number, Us.In the Fig. 2 below, let Ki = K2 = K and ti = t=t. %3D T -T X Fig. 2 (a) Let T= 0 °C and T= 200 °C. Solve for T: and unknown rates of heat flow in term of k and t. MEC_AMO_TEM_035_02 Page 2 of 11 Finite Element Analysis (MECH 0016.1) – Spring - 2021 -Assignment 2-QP (b) Let T- 400 °C and let fs have the prescribed value f. What are the unknowns? Solve for them in term of K, t, and f.The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: T and a, PND? b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750kg/m² and the dynamic viscosity is 0.2 N.s/m². For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s/m². kg.m IN =1
- Fit a power law model to the rheological behavior presented in the data: T [=]D/cm^2 y[=]1/2 1 3 2 - 3 30 4 52 5 80 6 100 7 130 8 160 9 175 10 190 11 218 12 240 13 265 (The second data in the table is not necessary to solve it.)Help yourself with matlab to solve it with the following formula: (Photo)The stress profile shown below is applied to six different biological materials: Log Time (s] The mechanical behavior of each of the materials can be modeled as a Voigt body. In response to o,= 20 Pa applied to each of the six materials, the following responses are obtained: 2 of Maferial 6 Material 5 0.12 0.10 Material 4 0.08 Material 3 0.06 0.04 Material 2 0.02 Material 1 (a) Which of the materials has the highest Young's Modulus (E)? Why? Log Time (s) (b) Using strain value of 0.06, estimate the coefficient of viscosity (n) for Material 6. Stress (kPa) StrainPide Use Buckingham's PI Theorem to determine non-dimensional parameters in the phenomenon shown on the right (surface tension of a soap bubble). The variables involved are: R AP - pressure difference between the inside and outside R- radius of the bubble Pide Soap film surface tension (Gravity is not relevant since the soap bubble is neutrally buoyant in air)
- CALCULATE THE FOLLOWING: We performed the experiment to measure MATERIAL 1 - BRASS the thermal conductivity of 2 materials (Brass & Steel) in the laboratory and measured the following tabulated values: Calculation for Brass Quantities Values Material 1- BRASS Calculated Power (Q') W (Diameter = 25mm) Area of cross section (A) m2 Power Difference in Temperature Temperature (°C) between two points (AT) °C Difference in distance between two points (Ax) m Q' 1 2 3 (W) Thermal conductivity of brass (kp) W/m°C 4 5 6 8 9. 14.65 79 77.4 76 50.1 46.5 42.4 36 34.5 33.6 MATERIAL 2 - STEEL Calculation for Steel Material 2 - STEEL %3D Quantities Values Calculated (Diameter = 25mm) %3D Power (Q') W Power Area of cross section (A) m2 Temperature (°C) Difference in Temperature between two points (AT) °C Q' 1 |(W) Difference in distance between two points (Ax) m 2 3 7 8 14.2 88.6 87.5 85 33.9 33.6 32.4 Thermal conductivity of steel (kg) W/m°CI1 Give an example how it is applied in molecular dynamics simulation and Monte carlo simulation? Typical distributions of particles in a volume (e.g. crystal structure for a solid, or distribution of masses and velocities in a “typical” galaxy) - Distributions of particle velocities/energies (e.g. Boltzmann distribution at a fixed temperature) - E.g. for a liquid it is common to start with a solid crystal structure and let the structure “melt” (by setting appropriate velocities corresponding to the liquid phase temperature!) - E.g. to setup a collision of two galaxies, you could try to generate a stable distribution of masses and velocities for a single galaxy first by performing a separate simulation -E.g. A simple model of a phase transition between a low temperature ordered phase (ferromagnet) and high temperature disordered phase (paramagnet) whats the difference in phase space in Molecular dynamics and Monte Carlo simulation?I just need help simplifying these equations (1 and 2). Qo,Kic, and CL are all their own variables (not 2 multiplied ie. Q*o, k*i*c and not C*L)
- (6) A dimensionless group called the Reynolds number is defined for a flow in a pipe or tube DV p NRe %3D uV/D Where V is the average velocity in the pipe, p is the fluid density, u is the fluid viscosity, D is the tube diameter. The second form of the group indicates that it is a ratio of the convective (turbulent) momentum flux to the molecular (viscous) momentum flux, or the ratio of inertial forces (which are destabilizing) to viscous forces (which are stabilizing). When viscous forces dominate over inertial forces, the flow is laminar and fluid elements flow in smooth, straight streamlines, whereas when inertial forces dominate, the flow is unstable and the flow pattern break up into random fluctuating eddies It is found that laminar flow in a pipe occurs as long as the value of Reynolds number is less than 2000. Calculate the maximum velocity and the corresponding flow rate (in cm'/s) at which lamina: tlow of water is possible in tubes with the following diameters: 0.64, 1.27,…Ql: The viscosity in industrial measurement continue to use the CGS system of Lunits, since centimeters and grams vield convenient numbers for many fluids. The absolute viscosity () unit is the poise, I poise = 1 gtem. s). The kinematic viscosity (v) unit is the stohes, I stokes = 1 em /s. Water at 20C has u = 001 poise and also V= 0.01 stokes. Express these resalts in (a) SI and (h) BG tanits.Q2 Consider a conical receiver shown in Figure 2. The inlet and outlet liquid volumetric flow rates are Fl and F2, respectiveily. ccorresponding radius in r) Figure 2 Conicul tank Develop the model equation with necessary assumption(s) with respect to the liquid height h. ii. What type of mathematical model is this? 1 R %3D Hint: Model: = F, – Fz, where the volume V=r h=nh, since = substitute V and Fz expressions and get the final form. %3D %3D %3D dt H.