Consider the boundary layer flow=1-(1-)1.5, 0
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- Solve using Euler's law the boundary representation model for the below-mentioned diagram.4-17 Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 4-16. The pressure field is given by P = Po 2U,bx + b°(x² + y°) where P, is the pressure at x = 0. Generate an expression for the rate of change of pressure following a fluid particle.1. Derive the 3rd Order, non-linear, Blasius equation, as shown in class F"" + 1/2 FF" =0 Explain the physical significance of each of the Boundary Conditions: a) E(n-0)-0 b) F'(n-0)-0 c) F'(n)-1
- :Write the correspond boundary conditions for the below one-dimensional configurations I, IoEngine oil at 60°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r). (Hint: P = Patm everywhere on the free surface. The flow is rotationally symmetric about the z-axis.)Q4) Set up the differential equations for the two masses [Fig.1] 2cos (3t) Fig. 1 C1 K1 M1 M2 K3
- The velocity potential for non-viscous two-dimensional and uncompressed water flow in Cartesian coordinates is given as D= -(3x²y - y³) a) Find the corresponding current function. b) Find the pressure difference between points (1,2) and (4,4). Omit the height differenceEx:O How many Potenhially defferent mixed tensors forder two ca be defined by faking the auer Product of s and T twice 7 Ok / tten Contraching sThe answer will be 9.554x10^-4 but I can’t figure out how to get there. Please use dimensional analysis
- (a) Show that in the limit kd < < 1 the pressure field (6.8.6) 2A p(r,0,t)~~—cos(kdsino)e r reduces to 2A j(wt-kr) p(r,0,t)~~—e r boundary? j(wt - kr) 9 (rigid boundary), 6.8.6 (b) What effect does the presence of the boundary have on the sound pressure level observed (many wavelengths away) for the same source in the absence of the4. Kittel Ch3-4. Energy fluctuations. Consider a system of fixed volume in thermal contact with a reservoir. Show that the mean square fluctuation in the energy of the system is ((x − (e))²) = t² (əU / ət), Here U is the conventional symbol for (e). Hint: Use the partition function Z to relate U/ar to the mean square fluctuation. Also, multiply out the term (...). (89)Q2:: Discuss the usefulness of Navier-Stokes equation with the help of practical examples.