The decay of a radioactive isotope can be theoretically modeled with the following equation, where C0 is the initial amount of the element at time zero and k is the decay rate of the isotope. Create a proper plot of the decay of isotope A [k = 1.48 hours]. Allow time to vary on the abscissa from 0 to = hours with an initial concentration of 10 grams of isotope A.
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- Case 1: Material system without density and viscosity differences Though unlikely in real life, in this case, we assume that all of the material in the homogenizer is of the same density and viscosity. Thus, only one set of material parameters are mentioned (density, ρ; dynamic viscosity, μ). The important parameters are listed as follows: Target quantity : Mixing time, θ Geometric parameters : Stirrer diameter, d Material parameters : Density, ρ Dynamic viscosity, μ Process-related parameters : Stirrer speed, n 1.1) Write out the relevance list for Case 1. 1.2) Generate the pi-set for this case. 1.3) Write out the appropriate pi (π) numbers from the generated pi-set. 1.4) Identify the established dimensionless numbers from the derived pi (π) numbers. 1.5) Write the possible relationship of the dimensionless numbers for Case 1.arrow_forwardThe processing of raw coal involves “washing,” in which coal ash (nonorganic, incombustible material) is removed. The article “Quantifying Sampling Precision for Coal Ash Using Gy’s Discrete Model of the Fundamental Error” (Journal of Coal Quality, 1989:33–39) provides data relating the percentage of ash to the volume of a coal particle. The average percentage of ash for six volumes of coal particles was measured. The data are as follows: Volume (cm3) 0.01 0.06 0.58 2.24 15.55 276.02 Percent ash 3.32 4.05 5.69 7.06 8.17 9.36 Using the most appropriate model, predict the percent ash for particles with a volume of 48 cm3. Round answer to three decimal places. * the answer i got was of 6.260 was wrongarrow_forwardThe dependence of thermal conductivity of a material on temperature is given by an empirical equation k = a ebT where a and b are constants, and k is in W/m-K and T is in K. Spot the true statement from the following set. a, a and b have the same dimension as k. b. a has the dimension of k and b is dimensionless. c. a and b are dimensionless. d. a has the dimension of k and b has the dimension of T.arrow_forward
- Geochemical Box Models - please use same terminology found in question Consider an element X exchanging between two geochemical reservoirs A and B. Let MA and MB be the masses of X in reservoirs A and B, respectively; let tA and tB be the residence times of X in reservoirs A and B, respectively. Further let M = MA + MB be the total mass of X in the two reservoirs combined. Consider a situation where additional mass M' is injected into reservoir A at time t=0 increasing the total amount of element X in the system from M0 to M1, with no further injection at later times; further assume that tA >> tB, that the total mass in the altered system is M1 = M0 + M', and that M0 << M'. Give an expression for MB(t) as a function of M1, tA, tB, and t. What is the characteristic time for MB to approach steady state? What is the characteristic time for MA to approach steady state?arrow_forwardYou are developing a porous membrane for use in a dialysis system. The membrane must be able to retain both protein and glucose on the inlet side and allow other, smaller molecules to flow through. You have found that the membrane is 0.25 mm thick and contains long, rectangular pores with a width of 0.1 microns. 57% of the 50 cm^2 membrane surface area is covered with pores. A test fluid (viscosity = 1.5 cP, density = 1015 kg/m^3) is passed through the membrane. You can assume that the test fluid has a composition similar to that of blood plasma. An initial test is run at physiological conditions, and you observe that the flow rate of fluid through the membrane is 500 cm^3/min. Given this data, what must the hydrodynamic pressure drop across the membrane in your test system be in pascals?arrow_forwardThe following table lists molecular weight data for a polypropylene material. Compute the number-average molecular weight, Molecular Weight Range (g/mol)//// xi////// wi 8,000–16,000//// 0.05/// 0.02 16,000–24,000 ///0.16// 0.10 24,000–32,000 ///0.24// 0.20 32,000–40,000 ///0.28// 0.30 40,000–48,000 ///0.20// 0.27 48,000–56,000 ///0.07// 0.11 Round your answer to 0 decimal places.arrow_forward
- 1. Circle weather the following statements are true or false. If the statement is true justify your reasoning if the statement is false correct the statement to make it true or justify why it is false a. Impulse is the integral of a force vs distance graph b. In two dimensions analyzing linear and angular momentum provides up to three scalar equations. c. Linear acceleration and angular acceleration both have units of ft/s^2 or m/s^2 d. When absolute motion or a rigid body it is important to find a function that relates linear and angular position then integrate to find velocity e. Instantaneous centers can only be determined for velocity and only for a snapshot in timearrow_forwardRefer to the Worksheet shown, set up to calculate the displacement of a spring. Hooke's law states that the force (F, in newtons) applied to a spring is equal to the stiffness of the spring (k, in newtons per meter) times the displacement {x, in meters): F= kx. ;Chapter 10, Problem 161CA, Refer to the Worksheet shown, set up to calculate the displacement of a spring. Hooke's law states Cell A3 contains a data validation list of springs. The stiffness (cell 83) and maximum displacement (cell C3) values are found using a VLOOKUP function linked to the table shown at the right side of the worksheet. These data are then used to determine the displacement of the spring at various mass values. A warning is issued if the displacement determined is greater than the maximum displacement for the spring. Use this information to determine the answers to the following questions. Write the expression, in Excel notation, that you would type into cell 86 to determine the displacement of the spring.…arrow_forward1) To ensure complete similarity, the model and prototype must be a) same material b) similar geometric and all independent groups are match c) same geometric d) in same fluid 2) Temperature is a dimension, kelvin is a unit. True or Falsearrow_forward
- In the field of air pollution control, one often needs to sample the quality of a moving airstream. In such measurements a sampling probe is aligned with the flow as sketched in Fig. A suction pump draws air through the probe at volume flow rate V· as sketched. For accurate sampling, the air speed through the probe should be the same as that of the airstream (isokinetic sampling). However, if the applied suction is too large, as sketched in Fig, the air speed through the probe is greater than that of the airstream (super iso kinetic sampling). For simplicity consider a two-dimensional case in which the sampling probe height is h = 4.58 mm and its width is W = 39.5 mm. The values of the stream function corresponding to the lower and upper dividing streamlines are ?l = 0.093 m2/s and ?u = 0.150 m2/s, respectively. Calculate the volume flow rate through the probe (in units of m3/s) and the average speed of the air sucked through the probe.arrow_forwardCardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph). Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24 Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text. Compute the least-squares line for predicting the long-term measurement from the short-term measurement.…arrow_forwardFor the Following question Graph all 4 : [I just need all 4 graphs and please explain and make clean solution] Position vs time Velocity vs time Acceleration vs time Force vs time [For your convenience, I have solved the numerical solutions for the problem] (Please Look at the picture since it is much cleaner) Question : A 550 kilogram mass initially at rest acted upon by a force of F(t) = 50et Newtons. What are the acceleration, speed, and displacement of the mass at t = 4 second ? a =(50 e^t)/(550 ) [N/kg] v = ∫_0^t▒(50 e^t )dt/(550 )= v_0 +(50 e^t-50)/550=((e^t- 1))/11 x = ∫_0^t▒(e^t- 1)dt/(11 )= x_0 +(e^t- t - 1)/(11 ) a(4s)=(50*54.6)/550= 4.96[m/s^2 ] v(4s)=((e^4-1))/11= 4.87[m/s] x(4s)=((e^4- 4 - 1))/11= 4.51 [m]arrow_forward
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