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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- t ) where A = 0 . 5 m 2 , L = 5 m , b = 0 . 1 m- 1 , = 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 is shown in the figure. It is known that the velocity is pure tangential,is shown in the figure....
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This note was uploaded on 05/12/2010 for the course MAE 101A taught by Professor Marsden during the Winter '10 term at San Diego.
- Winter '10
- Fluid Dynamics