Select the best numerical method to estimate the salt concentration and justify your answer. method 1: ruler's method
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The concentration of salt ? g/L in homemade soap is given as a function of time as follows: ??/dt = (0.37? − 0.03)? At the initial time, ? = 0 minute, the salt concentration is 20 g/L. Choose a step size in a range of 1 < h ≤ 1.5 minutes for the interval from 0 to 8h minutes and apply THREE (3) numerical methods to compute the salt concentration. Select the best numerical method to estimate the salt concentration and justify your answer.
method 1: ruler's method
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- For the diffusion coefficient K = 0, the above equation becomes: If known: The flow velocity is constant, U = 0.5 m/s Channel length 1000m Δx = 100m Δt = 1000 sec When t = 0, the concentration along the channel is zero [C(C,0) = 0] The boundary conditions along upstream & downstream are 2 & 0 respectively Calculate the above equation using the concentration C(x,t) & carry out until Time step k-5 with scheme: a. Explicit b. ImplicitDiffusion flux is directly proportional to the concentration gradient, according to Fick’s first law. Concentration gradient is________: A ) Rate of change of concentration with respect to distance B ) Rate of change of concentration with respect to time C ) Difference in concentrations at the source and sink D ) Ratio of concentrationsThe same engineer decides to look into rates of cooling for liquids toexperiment with different cooling solutions for servers. She finds thatthe rate of cooling for one liquid can be modelled by the equation:y = 48 × 0.99t(0 ≤ t ≤ 80)where y is the temperature of the liquid in degrees Celsius and t is thetime in minutes.(i) State whether the type of reduction for this model is linear orexponential. Describe how reduction rate differs between linear andexponential functions. (ii) Calculate the temperature when t = 20. [3](iii) Write down the scale factor and use this to find the percentagedecrease in the temperature per minute. (iv) Use the method shown in Subsection 5.2 of Unit 13 to find the timeat which the temperature is 30◦(v) Determine the halving time of the temperature.
- A study of the physical characteristic of honey was conducted due to thelarge demand of royal jelly. A capillary tube viscometer was used by aresearcher in determining the viscosity of the honey. The viscometer is250 mm long with an outside diameter of 55mm and effective thickness of2.5mm and was used horizontally so that the effect of gravity wasneglected. At an ambient temperature of 30oC the following data werecollected: ΔP (Pa) Q (cc/s)10.0 1.2512.5 1.5515 1.8017.5 2.0520.0 2.55 What will be the stress produced per unit length in the tube used in theproduction of royal jelly if it has a radius of 5mm and a flow of 1 capsuleper second. (1 capsule = 0.85 cc of royal jelly).The Reynolds number is a dimensionless group defined as follows for a liquid that flows through a pipe: Re = Dvρ / μ where D is the diameter of the pipe, v is the velocity of the fluid, ρ is its density and µ its viscosity. When the Reynolds number value is less than 2100, the flow is laminar, that is, the liquid it moves in lines of smooth flow. For Reynolds numbers greater than 2100, the flow is turbulent, characterized by considerable agitation. Liquid Methyl Ethyl Ketone (MEK) flows through 2067 '' ID tubing and through an average velocity of 0.48 ft / s. If the fluid temperature is 20 ° C, the density of the MEK The liquid is 0.805 g / cm and the viscosity is 0.43 cP (1 cP = 1.00 x 10 kg / (m-s)]. Determine the Reynolds number for MEK flow conditions. (Round the final result to a whole number without decimals).We would like to develop an empirical correlation to determine the heat trans- fer coefficient, h, for turbulent flow in a circular conduit. Please use the order provided for the lists of physical variables and fundamental units in working this problem. The following physical variables are to be included: h, average fluid velocity v, density ρ, viscosity μ, thermal conductivity k, specific heat capacity c, diameter D, and length L. (a) Express each physical variable in terms of fundamental units mass (m), length (l), time (t), and temperature (θ).
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- The temperature of an experimental heated enclosure is being ramped up from 80 to 450°F at the rate of 19°F/min. A thermocouple, embedded in a Thermowell for protection, is being used to monitor the oven temperature. The thermocouple has a time constant of 84 s. At t = 10 min, what is the difference between the actual temperature and the temperature indicated by the thermocouple? Final answer in whole number. Please show your complete solution and write readable.PROPAGATION OF ERROR You are tasked to supervise the design of 0.5MW wind turbine to be constructed in a Wind Farm in Pililla, Rizal. Suppose the design criteria are as follows: The air density as surveyed after 2 year period averaged at 1.225 kg / cubic meter. The sweeping diameter of the rotor blades is 125m, and the anemometer reading in the area amounts to 4.2m/s on a 2 year period of survey. if the diameter measurement is off by 0.1m and the anemometer reading is also fluctuating by 0.05m/s. In the design specifications given, if the actual measurement of power via the substation amounts to exactly 530kW and given that the windspeed is off by 0.05m/s, what could have been the error in the measurement of diameter? Your answer must be in 3 decimal places and in correct signs and measurement. Show complete solution in paper.You 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?