Name ______

ME363 Exam 1 / Spring 2007

Honor Statement:

Signed:______

Concept Questions: /40

Problem 1: ______/30

Problem 2: /30

Total: /100

For the Concept Questions, please the correct answer.

Given the following diagram for the definition of a fluid:

This figure is a depiction of the behavior of a fluid element under the action of a constant shear force.

Given this, if the viscosity of the fluid is somehow made to be zero, which of the following are true?

a.  The upper plate will accelerate forever.

b.  The magnitude of the fluid force on the lower plate is zero

c.  All of the fluid has a velocity of zero

d.  b and c above

e.  a and c above

f.  a and b above

The basic equations governing fluid mechanics:

a)  include conservation of angular momentum and the 2nd law of thermodynamics

b)  include conservation of mass and Hooke’s law

c)  include conservation of energy and the Ideal Gas Equation

For a Newtonian fluid,

a.  The shear stress is proportional to the velocity gradient in the flow direction

b.  The shear stress is proportional to the velocity gradient perpendicular to the flow direction

c.  The shear stress is proportional to the viscosity of the fluid

d.  b and c above

e.  a and b above

Examples of body forces and surface forces are:

a.  Gravitational forces are surface forces, pressure forces are body forces.

b.  Gravitational forces are body forces, shear forces are surface forces.

c.  Pressure forces are body forces, shear forces are body forces.

The following is true for the gradient operator:

a.  The gradient of pressure is zero for a fluid at rest.

b.  The gradient of pressure at the top of a swimming pool will be much smaller than at the bottom.

c.  The gradient of a scalar is a vector that points in the direction of maximum rate of increase of the scalar.

Which of the following accurately represents the distribution of absolute pressure on the surface indicated?

Consider the experiment shown below. The four lettered tanks contain air. The liquid (shaded) is water. If ΔPXY = PX-PY…

A 2ΔPAB = ΔPCD

B ΔPAB = 4ΔPCD

C ΔPAB = 2ΔPCD

D 4ΔPAB = ΔPCD

E ΔPAB = ΔPCD

Consider the two coordinate axes shown in the figure below:

To transfer from one coordinate system to the other, the following should be used:

a.  x = a-x’

b.  x =-x’-a

c.  x = x’-a

Imagine we are viewing the pipe from an Eulerian perspective. For the gas inside the pipe, involved in this steady flow situation, which is/are true?

a.  The density is a function of position

b.  The density of the gas is uniform

c.  The density of the gas is a function of time

Consider the conservation of mass equation:

In words, this equation reads:

a.  The fixed amount of mass in the control volume is balanced by the mass that leaves or enters the control volume.

b.  The rate of mass accumulation in the control volume is balanced by the net rate of mass flow out through the control surfaces

c.  The rate of mass flow into the control volume is balanced by the integrated mass flow out through the control surfaces

d.  The accumulation of mass in the control volume is balanced by the net rate at which mass flows in through the control surfaces


Problem 1: {30 points} A chamber contains a hinged plate that forms a barrier dividing two liquids. On the left is oil with a uniform density of ρoil = 700 kg/m3. On the right is a stratified oil-water-soap mixture that has a density varying linearly from ρoil = 700 kg/m3 at the top to ρwater = 1000 kg/m3 at the bottom. The plate could possibly pivot to the position indicated by the dotted line, however the compressed air has just the right value Pair to keep the gate in equilibrium in the vertical position as drawn. Determine the absolute pressure of the compressed air, Pair [Pa]. The chamber can be assumed to extend infinitely far into and out of the page. {hints: g = 9.81 m/s2, 1 Pa = 1 N/m2, 1 N = 1 kg-m/s2, 1 atm = 101325 Pa.}


Problem 2: {30 points} A bottle resembling a 2-liter soda bottle rests on its side. The bottle initially contains soda which has a density ρo = 62 lbm/ft3 = 1.9 slug/ft3. However, at time t=0, a chemical is introduced into the bottle. The chemical causes the soda to convert to a foam with a lower density. The density of the foamy fluid in the bottle for later times behaves as ρ=ρoexp(-t/τ), with τ = 0.5s. The fluid throughout the bottle can be assumed to have uniform density. The velocity profile of the exiting foam jet is given by the equation shown. Determine umax [ft/s]. Note that umax may depend on time; if it does, your answer should include the variable t. {hints: 1 ft = 12”, , }

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