Show that the velocity of an incompressible flow has zero divergence.

Consider the one-dimensional, incompressible flow through the circular channel shown. The velocity at section 1 is given by U5U0 1U1 sin ?t, where U0 520 m/s, U1 5 2 m/s, and ? 5 0.3 rad/s. The channel dimensions are L51 m, R1 50.2 m, and R2 50.1 m. Determine the particle acceleration at the channel exit. Plot the results as a function of time over a complete cycle. On the same plot, show the acceleration at the channel exit if the channel is constant area, rather than convergent, and explain the difference between the curves.

1.A) A fluid of density ρ=850 kg/m3 and viscosity µ=0,8 Pa s is completely filling the spacing h= 2 cm between two parallel horizontal plates of length 2,5 m and width 1 m . The upper plate is pulled at a speed of U while lower plate is fixed . In order to generate a laminar steady incompressible flow of fluid in the spacing at a rate of 0,85 kg/s determine total shearing force in the field.ANSWER:10 N 1.B) A fluid of density ρ=850 kg/m3 and viscosity µ=0,8 Pa s is completely filling the spacing h= 2 cm between two parallel horizontal plates of length 2,5 m and width 1 m . The upper plate is pulled at a speed of U while lower plate is fixed . In order to generate a laminar steady incompressible flow of fluid in the spacing at a rate of 0,85 kg/s determine Reynolds Number of flow using the spacing as the characteristic dimension.ANSWER: 2,125 1.C) A fluid of density ρ=850 kg/m3 and viscosity µ=0,8 Pa s is completely filling the spacing h= 2 cm between two parallel horizontal plates of…