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Unformatted text preview: MAE 101A: Introductory Fluid Mechanics Homework 6 Due Wednesday March 17, 5:00 PM Problem 1 The y component of velocity in a steady incompressible flow field in the xy plane is v = 2 xy ( x 2 + y 2 ) 2 Show that the simplest expression for the x component of velocity is u = 1 x 2 + y 2 2 y 2 ( x 2 + y 2 ) 2 Problem 2 The y component of velocity in a steady, incompressible flow field in the xy plane is v = Axy ( y 2 x 2 ), where A = 2 m 3 · s 1 and x and y are measured in meters. Find the simplest x component of velocity for this flow field. Problem 3 Consider the incompressible flow of a fluid through a nozzle as shown in figure. The area of the nozzle is given by A = A (1 bx ) and the inlet velocity varies according to U = U (1 e λt ) where A = 0 . 5 m 2 , L = 5 m , b = 0 . 1 m 1 , λ = 0 . 2 s 1 , and U = 5 m/s . Find and plot the acceleration on the centerline, with time as a parameter. Figure 1: Problem 3 Problem 4 Consider the incompressible, inviscid flow of air between two parallel disks of radius R = 75 mm , as shown in the figure. Air enters through a pipe of radius R i = 25 mm and exits radially, reaching R = 75 mm at a velocity V = 15 m/s . (a) Apply continuity equation and simplify the equation. 1 (b) From (a) show that ~ V = V ( R/r ) ~ e r , for R i < r < R . (c) Calculate the radial acceleration of a particle at r = R i and at r = R . Figure 2: Problem 4 Problem 5 The inviscid incompressible flow between two parallel disks rotating at an angular velocity ω is shown in the figure. It is known that the velocity is pure tangential,is shown in the figure....
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 Winter '10
 Marsden
 Fluid Dynamics, Velocity, Incompressible Flow

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