(a) Prove that the loss of pressure head for the viscous flow through a circular pipe is given by h. (b) Determine (i) the pressure gradient, (i the shear stress at the two horizontal parallel plates, and (iii) the discharge per meter width for the laminar flow of oil with a maximum velocity of 1.5 m/s between two horizontal parallel fixed plates which are 80 mm apart. Take viscosity of oil as 1.962 Ns/m2.

Thermo-Fluid

Consider a steady, laminar flow of an incompressible fluid through a channel of two infinitelylong flat plates (in x and z directions), with the lower plate (at y = −b) stationary andthe upper plate (at y = b) moving at a constant velocity of V0. A known, constant pressuregradient p′is applied in the x direction. Neglect the effect of gravity. Let the dynamic viscosityof the fluid be μ and density be ρ.   (a) Write down the component of the momentum equation you will use to solve for thevelocity profile u(y).(b) It is argued that the flow is fully developed. Is it true? Explain (briefly) why or whynot?(c) Is it safe to assume that the flow is two-dimensional? Why? What does it mean in termsof simplifying the equation?(d) Using appropriate assumptions, simplify the momentum equation clearly indicating whichterms drop out and why. Clearly indicate the boundary conditions needed to solve theequation.(e) Solve for u in terms of μ, b, V0, and p′.(f) Find the and expression for the power…