Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe of diameter D or radius R = D/2 inclined at angle a. There is no applied pressure gradient (@P/x = 0). Instead, the fluid flows down the pipe due to gravity alone. We adopt the coordinate system shown, with x down the axis of the pipe. Derive an expression for the x- component of velocity u as a function of radius r and the other parameters of the problem. Calculate the volume flow rate and average axial velocity through the pipe. 102 α Pipe wall Fluid: p. R X

find:v Maximum speed Average speed Volumetric flow Show that the speed profile provided satisfies the continuity equation in its differential format Incompressible steady flow in the inlet between parallel plates is uniform, Vo = 8 cm/s, while downstream, the flow develops into the parabolic profile = az(zo-z), where a is a x constant. What is the maximum value of v,? Vo

In an experiment to determine the force acting on an oval-shaped body, a model is mounted in the test section of a wind tunnel. The test section itself has rectangular cross section with height 2h and width l (into the page). The model spans the entire width of the test section. The model is subject to a steady, uniform, incompressible flow of velocity V₁. The pressure gauge indicates a pressure difference (Ap) between the test section exit (location 2) and the test section entrance (location 1). The velocity profile downstream of the model is shown in the figure. Use the control volume shown. Find the force acting on the model in terms of given quantities V₁, h, l, Ap, and density, p. Ap V AL

Need help on both parts please