Simulation of IV Bag Decanting

Simulation of IV Bag DecantingBase anatomy and equalitysThe lay outup of the simulation is disposed below. The tip in magazine at the top of the limpid in the IV adhesive friction is denoted with a subscript 1. The point at the exit of the catheter into the longanimouss arm is denoted with a subscript 2. assumptive that the patient does not move his/her arm during the procedure, we can set point 2 as a static, whereas point 1 is moving dynamically as the bulge empties.Bernoullis Equation in the units of energy is given asSetting point 2 as the eyeshade of ground, excluding the pumping verge and combining pressure sensation terms into a pressure difference, further beat P1 and P2 in gauge pressure and assuming P1 to be atmospheric yields the followers equationWhere WhereFor stratified catamenia (Re And for roiled (Re 2100)numerical DevelopmentDerivation of equations pertaining to the IV dishWhat is needed first is a way to find the spate of legato still within t he base of operations when only knowing the height of the fluid in the bag. Taking the rally axis of the bag as an independent covariant and viewing the spoke of the bag at that point as a dependent variable yields the following straight lineWhich has the equationAnd performing a hale of revolution ab fall out the h axisIt is know that and that by mound balance assuming no accumulation in the pipe butFinally for the frustum IV bagFriction terms development study the Reynolds number in the pipe and the catheterBut by circle balance and assuming no accumulationWhich is always less than one. and so if flow in the catheter is laminar, then flow in the pipe has to be laminar too.This leaves 3 groundss of flow in the system. The first is flow is laminar in the catheter and pipe. The befriend case is flow is steamed in the catheter, but laminar in the pipe, or flow is turbulent for the catheter and pipe.For the first case where flow is laminar in both the catheter and the pipe If the flow is turbulent in the catheter, then the friction term is the sum of the friction from the pipe and the catheterSimulation Program DevelopmentSolving pep pill of fluid deviation the catheter for any(prenominal) fluid height hThe above Equations 1-9 are mutely incorporated into matlab functions (Appendix A Calculations functions).The first problem that the program moldiness figure out is calculating the instantaneous velocity of fluid out of the catheter at any height of fluid in the IV bag.First the flow in the catheter is assumed to be laminar (this is just a starting point for iterations). The correct velocity of the fluid leaving the catheter is the point here Equation 1 is persistent.Since the equation contains a square root, for the answer to be commonsensible then in that respect has to be a positive root. i.eSubstituting equations 3 and 5Since is very dwarfish, its square whitethorn be omit (checked with given simulation values it was on the order of 10- 10)The velocity that satisfies the stable solution of Equation 10 must therefore lie in the midst of 0 and for laminar flow speeds. This means that Equation 10 may be solved by bisection rule, giving the instantaneous velocity out of the catheter for a true height of fluid in the IV bag.If the upper limit and minimum velocities do not generate the proper conditions required for the bisection method (one function value must produce a number greater than nada, and the other must generate a number below zero to imply a root between the two numbers on a continuous function), then the flow velocity must be such that the flow is turbulent in the catheter.If it is the case that flow must be turbulent in the catheter, then we can set an sign guess of v2 at the minimum velocity required to have turbulent flow in the catheter. Using this as an sign velocity, it can be iterated until a stable solution is found.See Appendix B for this programming logical system. Comments have been adde d to aid understanding.Fluid flow out of the IV bagIn order to calculate how fluid flows out of the IV bag, we set the program to take small clip fixingss and determine the velocity of the fluid flowing out of the catheter for a set fluid height. Since that time element is small, we assumed that the velocity did not interchange appreciably in that small element. Volumetric flow is the product of linear velocity of flow and cross-sectional surface area, and assuming no accumulation in the pipe for sess balanceNow we need to know what the height is of the bag for that volume, which is precisely the real root that solves Equation 2.This entire process is iterated for each time element until the bag empties or the fluid velocity leaving the catheter is zero.This logic may be found in Appendix C.Concatenating ResultsFinally a matrix is constructed that holds all data of the catheter fluid velocity, bag volume, fluid flow rate and height of fluid in the bag and is concatenated with a time vector. This resultant matrix now holds all of the data of the simulation, which is parsed to the primary clear that is running the simulation to produce the represents, and find numerical values for points on the graphs.Results of SimulationThe following data was fed into matlabP2 = 90.228/760*101325Lcat = 43.703/1000Dcat = 0.711/1000Lpipe = 1.383H = 22.8/100R = 0.3829*Hhd = 1.377Dpipe = 3/1000rpipe = 0.5*Dpipemu = 1.142/1000rho = 1017X = calcX(R,H,rpipe)h0 = 0.8*Xbeta = (R-rpipe)/XThe simulation was run using the following command to retrieve the results matrixVhvQt = generateVhvtQMatrix(rho,Dcat,mu,Lpipe,Lcat,Dpipe,beta,h0,rpipe,9.81,hd,P2)Solution graphs were maculationted as followsplot(VhvQt(5,),VhvQt(2,))xlabel(Time in seconds)ylabel(Height of fluid in bag in meters)Bag volume is course of study 1, height of bag is actors line 2, velocity of fluid in the catheter is row 3, flowrate is row 4 and row 5 is the time vector. To find the original time taken for the bag to empty, the command was applyVhvQt(5,end)= 3122Similar commands were used to find exact datapoints at any period in time. countersign of Simulation ResultsThe values of the viscosity and density of the 5% w/v glucose solution more commonly known as D5W, Dextrose 5 Water or Intravenous Sugar Solution, were looked up from Wolfram alphas material database, and had the values of and . (Wolfram Alpha)The purpose of the simulation was to calculate and plot the graphs as well as answer how long it takes for the bag to drain.It took 3122 seconds for the bag to drain, or just over 52 minutes. At the last second of the simulation, the height of fluid in the bag was less than 4 millimetres, which corresponds to a volume of 0.045 mL. Figures 3-5 all show a negative exponential function, which is to be expected since the flow rate is a function of the head pressure, which is a function of the conical shape of the bag. Initially, the high flow rate that corresponds with the high head of fl uid does not change very much, as the take of fluid in the cone does not drop significantly quickly. However, afterward about 2500 seconds (80% through the time of the simulation), the velocity of fluid leaving the catheter begins to change. magic spell this change is clearly not linear, it is not really significant when compared to the dictatorial changes in values. From the start of the simulation until 80% through the simulation (2500 seconds), the velocity of fluid in the catheter only changes from 0.8655 to 0.6922 m/s, or 20.02%. It is only in the last period of time just before the bag empties is there a significant change in the velocity of fluid launching the patient, with the final velocity being 0.4707 m/s just as the bag empties, which is itself only a change of 45.62%.This phenomenon is most apparent in Figure 6, where it can be seen that the volume of fluid left in the bag appears to decant at an almost linear rate (differential of volume/time is flow rate). Only ju st after 2500 seconds does the steepness of the graph very slightly begin to change upward indicated a slow in the flow rate of fluid leaving the bag.This phenomenon does, however, make sense. The height that the bag is lifted above the catheter is hd = 1.377 meters. The height of fluid in the bag at the start of the procedure is h0 = 0.1793m, or only 13.20% of hd. The means that the driveway force behind the IV procedure (which is the height above the IV bag is placed above the catheter in the patients arm) that creates the pressure difference to overcome the venous pressure of blood in the patients veins only changes by 13.2%, and remains changed by only 20.02 % during the initial 80% of the procedure in other words, it doesnt change by much, and therefore we expect that the flow rate wont change very much until very close to the end of the procedure, which is what we see in Figure 3.In real world application, this means that in ecumenical the flow rate of IV solution to the pa tient is mostly a function of how high above the patient the IV bag is placed, and not necessarily how empty or full the bag its self is. In fact, general practise used by doctors is simply to place the IV bag above the heart level of the patient (Dr. Chen-Maynard, 1999). In application, a desired flow rate of IV fluid into the patient may controlled by lowering or lifting the IV bag a certain height above the patient.NomenclatureReferencesDr. Chen-Maynard, P. R. (1999). Calculating Parenteral Feedings. calcium California Department of Health Science and Human Ecology.Wolfram Alpha. (n.d.). Comprehensive clobber Data Sheet for D5W. Retrieved April 28, 2014, from http//www.wolframalpha.com/input/?i=5%+(w/v)+glucose