In making a dimensional analysis, what rules do you followfor choosing your scaling variables?
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In making a dimensional analysis, what rules do you follow
for choosing your scaling variables?
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- QI (a) Sketch the dimension in Figure Q1 (b) below (front view) by refferring the Figure Q1 (a) using standard practice. Figure Q1 (b) 8.0 27.0 D 5.0 24.0 Figure Q1 (a) 10.0Dimensional analysis concept applied hereGive Justification for performing a geometrically scaled model rather than the full-scale prototype in the technique of dimensional analysis and similarity.
- how to solve dimensional analysis problemsThe 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 =1What is dimensional homogeneity?
- Write the primary dimensions of each of the following variables, showing all your work: (a) specific heat at constant pressure cp; (b) specific weight; (c) specific enthalpy h. and (d) specific gas constantSome children are playing with soap bubbles, and you become curious as to the relationship between soap bubble radius and the pressure inside the soap bubble . You reason that the pressure inside the soap bubble must be greater than atmospheric pressure, and that the shell of the soap bubble is under tension, much like the skin of a balloon. You also know that the property surface tension must be important in this problem. Not knowing any other physics, you decide to approach the problem using dimensional analysis. Establish a relationship between pressure difference ΔP = Pinside − Poutside, soap bubble radius R, and the surface tension ?s of the soap film.Force F is applied at the tip of a cantilever beam of length L and moment of inertia I Fig. . The modulus of elasticity of the beam material is E. When the force is applied, the tip deflection of the beam is z d.Use dimensional analysis to generate a relationship for zd as a function of the independent variables. Name any established dimensionless parameters that appear in your analysis