Download AMEE 202 Midterm S14_1 Group 2

Department of Mechanical Engineering
SUBJECT: AMEE 202 - FLUID MECHANICS I
DATE: 8 April 14
TIME: 90 Minutes
INSTRUCTIONS TO CANDIDATES:
Answer all questions from Section A and two questions from Section B.
All necessary work must be shown. Wherever needed:
 H 2O  1000 kg/m3 , H2O  1.15  10-3 Pa  s,  air  1.225 kg/m 3 , air  1.79  10 5 kg /(m  s )
g=9.81 m/s2 , patm  1.01  105 N/m 2 , 1.0 in= 0.0254 m, 1 ft=12 in, R  286.9 J/(kg K)
__________________________________________________________________
SECTION A
QUESTION 1 [20 Marks]
Fluid with mean velocity 5 m/s flows over a sphere to produce the flow pattern shown
on the left figure. The same fluid flows over a sphere half the size of the original
sphere and produces the same flow pattern (right figure).
a. State whether the flow is laminar or turbulent and explain
b. Determine the velocity of the fluid on the latter case.
QUESTION 2 [20 Marks]
The tank shown on the figure contains a liquid of density  . State whether the
following statements are true (T) or False (F), and give the correct answer if the
latter. (Note: pg denotes gauge pressure).
patm
z
g
A
z
i.
z h/ 2
v.
ii.
FR  ( patm  gh / 2)hb
vi.
iii.
iv.
pA  pgA  patm
vii. pg is gauge pressure
viii. The gauge pressure at the
surface is patm
pA   gh  patm
The gauge pressure at the
bottom is equal to  gh
The net force acing on the
side is equal to  gh 2b / 2
SECTION B
QUESTION 3 [30 Marks]
A hot air balloon weighs 230 kg , including the weight of the balloon, the basket and
one person. If the density of the hot air inside the balloon is in  1.04 kg/ m 3 ,
determine the required volume of the balloon to support the weight. If the balloon had
4
a spherical shape  V   r 3  , what would be the required diameter?
3


 in
out  1.18 kg/ m 3
QUESTION 4 [30 Marks]
A static thrust stand as sketched in the figure is to be designed for testing a jet
engine. The following conditions are known for a typical test:
i. Intake air velocity = 200 m/ s
ii. Exhaust gas velocity = 500 m/ s
iii. Intake cross-sectional area = 1 m 2
iv. Intake static pressure = 22.5 kP a
v. Intake static temperature = 268 K
vi. Exhaust density= 0.515 kg/ m 3
Estimate the mass flow rate and the volumertric flow rate at the exit.
Note: the ideal gas equation of state is p   R T where p is the absolute pressure.
QUESTION 5 [30 Marks]
The viscosity of liquids can be measured through the use of a rotating cylinder
viscometer of the type illustrated in the figure. In this device the outer cylinder is fixed
and the inner cylinder is rotated with an angular velocity,  . The torque T required
to develop  is measured and the viscosity is calculated from these two
measurements. If the liquid under testing is oil with   0.1 N s/m2 determine the
torque
developed
if
the
inner
cylinder
rotates
with
  200 rpm,  15 cm, Ro  7 cm, Ri  6.5 cm . Neglect end effects and assume the
velocity distribution in the gap is linear.
a. Find the velocity of the surface of the inner cylinder
b. Find the Shear Stress on the inner cylinder.
c. Find the total force acting on the inner cylinder, and the Torque.
T