Fluid enters a square duct as shown in the figure below. Considering boundary layer is laminar, please use the "displacement thickness" to estimate (a) the velocity Ucore and (b) the pressure Pcore in the core of the flow at the position x. U。。 Square Duct Boundary layers x Ucore
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- An oil film drains steadily down the side of a vertical wall, as shown on figure below. After an initial development at the top of the wall it attains a fully-developed draining vertical oil- film wherein the film becomes independent of "z" and of constant wall thickness. Let the vertical velocity as (w) and using the nomenclatures in the figure such as distance from plate (x), fluid properties, gravity (g) and film thickness ( ). Perform dimensional analysis and determine the function in terms of dimensionless parameters.An incompressible fluid flows past an impermeable flat plate, as in Fig. . , with a uniform inlet profile u = U, and a cubic polynomial exit profile (3η - η' where n= 2 Compute the volume flow Q across the top surface of the control volume. Ug у 3б Q? Uo y=0 CV Cubic Solid plate, width b into paperConsider steady, incompressible, laminar, fully developed, planar Poiseuille flow between two parallel, horizontal plates (velocity and pressure profiles are shown in Fig. At some horizontal location x = x1, the pressure varies linearly with vertical distance z, as sketched. Choose an appropriate datum plane (z = 0), sketch the profile of modi fied pressure all along the vertical slice, and shade in the region representing the hydrostatic pressure component. Discuss.
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