Demonstrate that Equation 6.16, the expression defining true strain, may also be represented by ET = In Ao A₁ when specimen volume remains constant during deformation. Which of these two expressions is more valid during necking? Why?

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. Implicit

Derive the basic mechanics solutions for the hoop stress (Subscript[\[Sigma], \[Theta]]) and the shear stress (Subscript[\[Sigma], r\[Theta]]) as functions of Subscript[\[Sigma], 0], a and b, r & \[Theta]. Derive the analytical linear elasticity solutions for the radial stress (Subscript[\[Sigma], r]), the hoop stress (Subscript[\[Sigma], \[Theta]]) and the shear stress (Subscript[\[Sigma], r\[Theta]]) as functions of Subscript[\[Sigma], 0], a and b, r & \[Theta].

Solve for u4x and u4y in (mm): Given: rax = 47.6314(kN) Tay rày = 27.5(kN) Solve: rax = 10°[23.9065u4x – 3.089u4y] Tay = 10°[-3.089u4x + 16.8378u4y]

(e) Given that Tij = 2µE¡j+λ(Ekk)³ij, show that (b) W = 1⁄T¡jEjj = µEijEij+(Ekk)² P = TT= 4u²EE+(E)²(4μλ +32²)

P2, µ2 2h P1 Po ρ1, μι L Figure 3: Two layer flow for (b) (b) Consider two immiscible (do not mix) fluid layers with different densities and viscosities which glide smoothly between two parallel horizontal walls, as shown in figure 3. Let pı and p2 be the densities and µ1 and µ2 be the viscosities of the two fluids, respectively. The flow is the result of an imposed constant pressure gradient, 2, similar to that of the Poiseuille flow. Assume a steady, incompressible, parallel viscous flow with p1 > P2 and µi > µ2- (i) Using the Navier-Stokes equations find the velocity profiles of both fluids. (ii) Ensure the fluid obeys the following conditions: The shear stress is continuous at the interface between the two fluids. • The velocity profile is continuous at the interface between the two fluids. No-slip boundary at the walls. (iii) Sketch the velocity profile. (iv) Determine where the maximum velocity occurs and explain why. (Hint: think about the respective viscosities and densities).…

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PROBLEM 3: A pole AB is being lifted using cables BC and BD. The pole is tilted at an angle of 60⁰ from the horizontal (from xy-plane) and the tensions in BC and BD are 26.1 and 11.3 kN, respectively. [7] Determine the coordinates of B. Answer format: (x, y, z) (ANSWER: 6.00, 0.00, 10.39 m) [8] Calculate the magnitude of the resultant of the two tensions BC and BD acting at B. (ANSWER: 36.04 KN) [9] Calculate the directional angle of the resultant of tensions BC and BD acting at B with respect to the z-axis (γ). (ANSWER: 135.969⁰) and with respect to the y-axis (β). (ANSWER: 103.611⁰).

Please hand Wright

Take substantial derivative of desity equation    ro = (t^(2 / 3)) + (x ^ 2) - y at (x, y, t) = (1, 1, 1)