State the following laws as applied to Biological fluid in membrane. i. Stoke's law ii. Nernst law equation

Have portions of part A and B complete, however I'm not sure on how to graph the phase potraits along with the inital conditions. Ultimately needing help with parts a through c thanks!

Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature; that is, F = -KVT, which means that heat energy flows from hot regions to cold regions. The constant k is called the conductivity, which has metric units SS S of J/m-s-K or W/m-K. A temperature function T for a region D is given below. Find the net outward heat flux boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral. Assume that k = 1. T(x,y,z) = 100 - 5x+ 5y +z; D = {(x,y,z): 0≤x≤5, 0≤y≤4, 0≤z≤ 1} The net outward heat flux across the boundary is (Type an exact answer, using as needed.) -KSS S F.ndS = -k VT n dS across the

3. The 25 mm diameter rod is subjected to the loads shown. Determine the state of stress at point A and B 75 mm 375 N 350 N 200 mm 450 N C

Determine the integrating factor of y = 2xy 2e 2x 2x e Option 3 O Option 1 None of the choices O Option 2

Develop an equation relating the rates at which the variables V and h are changing (dv/dt and dh/dt). O dV A) 9πh ² (dh) == dt OF O B) dV dt C) dv dt Bla TC == OD) D) dv dt 9 dv = = 3πr² WIN (dh) 3 h² ² (dh) p2 (dh)

b) An aircraft is performing a steady manouevre in level flight (horizontal plane). Indicated body rates (p, q, r) are (0,1.5, 2.6) degrees per second. Calculate the Euler yaw rate v and the aircraft roll and pitch attitudes o and 0. (101

The drag force, Fp, acting on an immersed body by a moving fluid can be calculated as PU? 2 where C, is the drag coefficient, A is the projected area of the body on a plane normal to the Fp = CpA flow, p is the mass density of the fluid, and U is the undisturbed velocity of the fluid. Suppose Cp, A, and p are known constants of values 0.6, 10 ft2, and 1.94 slug/ft, respec- tively. U is a lognormal random variable with parameters hy and Sy. Determine the distribution of Fp-

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

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