2. Sketch the streamlines for the flowv = -ay,w = 0,u = ax,where a is a positive constant. Next, let the concentration of some pollutant in the fluidbe:c(x, y, t) = ßx²yet,for y>0, where ß is a constant. Does the pollutant concentration for any particular fluidelement change with time?An alternative way of describing any flow is to specify the position x of each fluidelement at time t in terms of the position X of that element at t= 0. For the above flowthis Lagrangian' description isx = Xeat,y = Yeatz= Z.Verify by direct calculation thatdu= u,ốtDuDtin this particular case. Why are these results true in general?

Given the velocity is u=αx, v=-αy, w=0 and Lagrangian description is x=Xeαt, y=Yeαt, z=Z

Answered: 2. Sketch the streamlines for the flow…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Let z = f (x, y) = x² — y. Form implicit equation for the level curves (contours) at z = −2, −1, 0, 1, 2. and graph the equations.
,, ,,
Task VI: You are working in the fluid mechanics system engineering department at a firm. You have a task to determine flow rates of different valves that used to fill a tank. The tank is 2000 L that is fed by three valves with different flow rates. The flow rates (in L/min) of the three valves are x, y, and z. The three valves can be used to fill the tank in 3 scenarios. In the first scenario the three valves will fill the tank as follows, valve x will be opened for 10 mins, valve y for 4 mins, and valve z for 40 mins. Second scenario, the valve x opens for 15 mins, valve y for 2 mins, and valve z for 20 mins. Third scenario, valve x opens for 12 mins, valve y for 10 mins, and valve z for 15 mins. 2000L Tank Knowing that the tank's volume (v=2000L) as a function of three valves' flow rate is given by: x * C + y * D +z * E = 2000 L Where x, y and z represent the 1st, 2nd, and 3rd valve flow rates (L/min), C is the opening time for x valve (min), D is the opening time for y valve (min),…
Find the mass M of a fluid with a constant mass density flowing across the paraboloid z = 36 - x² - y², z ≥ 0, in a unit of time in the direction of the outer unit normal if the velocity of the fluid at any point on the paraboloid is F = F(x, y, z) = xi + yj + 13k. (Express numbers in exact form. Use symbolic notation and fractions where needed.) M = Incorrect 31740πσ > Feedback Use A Surface Integral Expressed as a Double Integral Theorem. Let S be a surface defined on a closed bounded region R with a smooth parametrization r(r, 0) = x(r, 0) i + y(r, 0) j + z(r, 0) k. Also, suppose that F is continuous on a solid containing the surface S. Then, the surface integral of F over S is given by [[F(x, y, z) ds = = D₁² Recall that the mass of fluid flowing across the surface S in a unit of time in the direction of the unit normal n is the flux of the velocity of the fluid F across S. M = F(x(r, 0), y(r, 0), z(r, 0))||1r × 1e|| dr de F.ndS X
The following table represents collected data from literature regarding the inelastic axial capacity (Pn) of Aluminum symmetric profiles as a function of the Area of the section and the Slenderness Ratio (SR) of the bar. Produce a linear model for the capacity in the form Pn= C1 X Area + C2 X SR, show the statistics of the linear model on this paper. Use your linear model to predict Pn for the case of Area= 200 and SR = 35. Produce a 95% confidence interval for your expected value of Pn at Area=200mm2 and SR=35. Find the maximum possible Pn and the minimum possible Pn based on 95% confidence limits of the parameters. Suggest how to improve your model by saying which one of the two factors must be treated nonlinearly and show why you think so! (give at least one direct reason) Area (mm2) SR (-) Pn (kN) 198.3 16 1273 216.3 89 136.5 228 94 129 184.3 83 133.8 220.1 99 112.3 166.7 33 765.4 201.5 70 205.6 219.8 53…
Solve this please
Find the equation of the line through the origin auel normal to the line x=y-S,2:2y-3?

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