Consider the following equation: 1 dollar bill ≈ 6 in. Is thisrelation dimensionally inconsistent? Does it satisfy thePDH? Why?
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Consider the following equation: 1 dollar bill ≈ 6 in. Is this
relation dimensionally inconsistent? Does it satisfy the
PDH? Why?
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Solved in 2 steps
- Q2/ By using the power series method make a dimensional analysis for the following variables: The frictional torque of a disc T = f (disk diameter D, rotating speed N, viscosity of fluid µ, and its density p).Pide 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)The following operations may be done on a dimensionless product to obtain other another product without losing its non-dimensionality EXCEPT: a.Adding it to another dimensionless product b.Multiplying it by another dimensionless product c.Impose a constant exponent on it d.Multiplying it by a constant
- m, zm 2. Two particles of equal masses move on a frictionless harizontal surface. Their center of kr? mass is fixed and their potential energies are krž and Also, they interact with each other with potential 2 akr2 Ris the distance between the masses, and k and a are positive constants. a. Find the Lagrangian in terms of the center of mass position CM, R and the relative position r. b. Solve the Lagrange equations for the relative coordinates X,Y and x,y. c. Explain the physical outcome of the results obtained in b.A bullet is to be tested in the laboratory to determine the drag force on it. Dependent parameter the drag force D (Newton) depends on the velocity of the bullet V(m/s), the length of the bullet L(m), sound velocity c(m/s), density of fluid ρ (kg/m3) and dynamic viscosity µ(kg/ms). Solve the problem by making the necessary assumptions and drawing the schematic figure. I-Determine the nondimensional p parameters using repeating variables ii-a bullet with a speed of 96,2 m/s in air may be modelled in a water tunnel with a test section velocity of 262 cm/s. Determine the length of the model, if the length of the bullet is 56,2 mm. The air and water temperature is 20 oC degree at 1 atm. iii- if the drag force on the model is measured to be 2,62 N, then determine the expected drag force on the bullet. Comment on dynamic similarity equivalence?Q2/ By using the power series method make a dimensional analysis for the following variables; The frictional torque of a disc T- f(disk diameter D. rotating speed N, viscosity of fluid u, and its density p).
- GIVE ME THE COMPLETE SOLUTION FOR THISTHIS IS THE ANSWER ACC TO THE ANSWER KEY I JUST NEED HELP FOR THE SOLUTION Theta3/T = ((5*s^2 + 9*s + 9))/(15*s^5 + 47*s^4 + 117*s^3 + 161*s^2 + 81*s)Answer all the questions 1) Using dimensional equations, convert: 700 m* /(day. kg) to cem* /(min. g). 2) Convert 210 X 10 kJ/min to hp 3) Calculate the weight in lbr of a 30.0-lbm object. 4) Calculate the mass in kg of an object that weighs 25 Newton. 5) The density of a fluid is given by the empirical equation: p = 70.5 exp(8.27 x 10-7P) where p is density (Ib/ft) and Pis pressure (lb,/in.?). (a) What are the units of 70.5 and 8.27 x 10-7? (b) Calculate the density in g/cm for a pressure of 9.00 x 10 N/m?. 6) The vapor pressures of 1-chlorotetradecane at several temperatures are tabulated here. T(C) 98.5 131.8 148.2 166.2 199.8 215.5 p* (mm Hg) 1 5 10 20 100 60 Use two different method to estimate the value of P' at T = 190 °C (7) The specific gravity of gasoline is approximately 0.70. a- Determine the mass (kg) of 50.0 liters of gasoline. b- The mass flow rate of gasoline exiting a refinery tank is 1150 kg/min. Estimate the volumetric flowrate in liters/s.Here are these questions if I could get help with themIf a spherical storage tank holds 40,000 gallons (120,000 liters) of water,what diameter must it have?If a cylindrical storage tank has a 40-foot (12 m) diameter circular 05::=how high must it be to hold 1 million gallons (3 million liters)?If water is moving at a rate of 3.2 ft3/sec (90,000 cc/sec), how manygallons (liters) per minute is this?If the specific gravity of gold is 19.0. what is the weight of a cubic inch(cubic centimeter) of gold? A cubic foot (cubic meter)?
- 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) 10.0Some 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.The mass of a flid stem is 0.311 slu, ts density is 30 l/ft' and the force of gravityis at 31.90 fps". Fin (a) the secfic olume in cm'/g,(b) the specfic weight ke/m', and (c) the total volume in in'. Solve the following problems SYSTEMATICALLY, enclose your final answers in a box, and Please write clearly. Thanks.