Mechanical Engineering Ph.D. Prelim. Qualifying Exam.
Fluid Mechanics, January 2004
You are required to do four out of five problems.
Clearly indicate which four problems you are selecting. Show all the work on exam sheets provided.
Write your student ID on each sheet. Do not write your name on any sheet.
Student ID Number:------
5. A small round object is tested in a 1.2 m diameter wind tunnel. The pressure is uniform across section 1 and 2. The upstream pressure at section 1 is 25mm H2O (gage), the down stream pressure at section 2 is 10mm H2O (gage). The mean air speed is 12 m/s. The velocity profile at section 2 is linear. It varies from zero at the tunnel centerline to maximum at the tunnel wall. Calculate (a) the mass flow rate in tunnel (b) maximum velocity at section 2 (c) Drag force of the object. Neglect viscous forces.
Mechanical Engineering Ph.D. Prelim. Qualifying Exam.
Fluid Mechanics, January 2004
You are required to do four out of five problems.
Clearly indicate which four problems you are selecting. Show all the work on exam sheets provided.
Write your student ID on each sheet. Do not write your name on any sheet.
Student ID Number:------
4. A liquid layer separates two plane surfaces as shown. The lower surface is stationary and upper surface moves downward at constant velocity V. The moving surface has width w, perpendicular to the plane of diagram and w>L. The incompressible liquid of density, ρ, is squeezed from between surfaces. Assume flow is uniform at any cross section and neglect viscosity as a first approximation Use a suitably chosen control volume to show that u= Vx/b, within the gap, where b= b0 –Vt. Obtain an algebric expression for the acceleration of a particle located at x. Determine the pressure gradient, ,, n the liquid layer. Find the pressure distribution, p(x).Obtain an expression for the net force that acts on the upper (moving) flat surface.
Mechanical Engineering Ph.D. Prelim. Qualifying Exam.
Fluid Mechanics, January , 2004
You are required to do four out of five problems.
Clearly indicate which four problems you are selecting. Show all the work on exam sheets provided.
Write your student ID on each sheet. Do not write your name on any sheet.
Student ID Number:------
3. A stream of air at standard conditions from a 5cm diameter nozzle strikes a curved vane as shown. A stagnation tube connected to a water filled U-tube manometer is located in the nozzle exit plane. Calculate the speed of air leaving nozzle at section 1. Estimate the horizontal component of force exerted on the vane by jet.
Mechanical Engineering Ph.D. Prelim. Qualifying Exam.
Fluid Mechanics, February 2004
You are required to do four out of five problems.
Clearly indicate which four problems you are selecting. Show all the work on exam sheets provided.
Write your student ID on each sheet. Do not write your name on any sheet.
Student ID Number:------
1. A ship is stuck on a bank. Find the shear force Fx and lifting force Fy per unit length of ship, when a wave arrives at the left side of the ship ( See figure). The dimensions are shown in the figure. The shape of the ship is given by: y= ax2.
Mechanical Engineering Ph.D. Prelim. Qualifying Exam.
Fluid Mechanics, January 2004
You are required to do four out of five problems.
Clearly indicate which four problems you are selecting. Show all the work on exam sheets provided.
Write your student ID on each sheet. Do not write your name on any sheet.
Student ID Number:------
2. A steady flow of ideal fluid around a cylinder of radius R has the potential function given by:
,
where u is the velocity of upstream flow. Find the pressure gradient at the point x=0, y=R