Problem 8.195
[Difficulty: 2]
Given:
Flow through a venturi meter (NOTE: Throat is obviously 3 in not 30 in!)
Find:
Flow rate
Solution:
Basic equation
C At
mactual =
4
(
C At
)
2 p 1 p 2 =
2 p
Note that mactual is mass flow rate (the
software cannot ren
Problem 12.59
[Difficulty: 2]
Given: Find: Solution:
Basic equation:
Scramjet-powered missile traveling at fixed Mach number and altitude Stagnation and dynamic pressures
k
c
k R T J kg K
M
V c M 7
p0 p
1
k1 2
M
2
k 1
SL 0.2377
p dyn slug ft
3
1 2
V
Problem 12.85
[Difficulty: 2]
Given: Find: Solution:
Basic equations:
Air flow leak in window of airplane Mass flow rate
1
mrate V A
Vcrit
2 k k1
R T0
0 crit
k 1 k 1 2
The interior conditions are the stagnation conditions for the flow Given or availabl
Problem 13.19
Given:
Isentropic air flow in converging nozzle
Find:
[Difficulty: 2]
Pressure, speed and Mach number at throat
Solution:
Basic equations:
k
T0
T
k1
1
2
M
p0
2
p
1
k1
2
p 1 350 kPa
m
V1 150
s
k 1.4
Given or available data
R 286.9
M
2
k 1
Problem 13.43
[Difficulty: 4]
Given: Find: Solution:
Basic equations:
Ideal gas flow in a converging nozzle Exit area and speed
k k 1 k 1
T0 T
1
k1 2
M
2
p0 p lbm ft
3
1
k1 2
M
2
1 k 1 M2 A 1 2 k 1 Acrit M 2
A1 1 ft c1
2
2 ( k 1)
Given or available
Problem 13.69
[Difficulty: 2]
Given: Find: Solution:
Basic equations:
Normal shock near pitot tube Air speed
k
p 1 p 2 1 V1 V2 V1
(Momentum)
p0 p
1
k1 2
M
2
k 1
p 2 8 psi
Given or available data T1 285 R k 1.4
p 1 1.75 psi Rair 53.33 ft lbf lbm R
p 02
Problem 13.97
[Difficulty: 3]
Given: Air accelerating through a converging-diverging nozzle Find:
Pressure ratios needed to operate with isentropic flow throughout, supersonic flow at exit (third critical); isentropic flow throughout, subsonic flow at exi
ME 309 Fall 2012 Exam 2
Problem 1 (20 points)
A. (4 pts) The total force experienced by the two plates (shown below) submerged in the water
can be resolved into two components Fx and Fy in the x and y directions, respectively.
Assume the widths of the two
ME 309 Fall 2012 Exam 2
Problem 2 (35 points)
A cart with frictionless wheels is equipped with an adjustable angle vane and is initially at rest.
A steady water jet from a stationary nozzle hits the vane horizontally from the left and leaves at
an angl
Problem 12.37
[Difficulty: 2]
Given: Find: Solution:
Basic equation:
Echo heard while hammering near mountain lake, time delay of echo is known How far away are the mountains
c
k R T
Assumption: Speed of light is essentially infinite (compared to speed of
Problem 12.27
[Difficulty: 2]
Given: Find: Solution:
Basic equation:
Submarine sonar Separation between submarines
c
Ev SG 1.025 c 1537 m s L 5 km x 2.5 km Ev 2.42 GN m
2
Given (and Table A.2) data
t 3.25 s c Ev SG w
kg w 1000 3 m
For the seawater
Hence t
Problem 9.13
Given:
Laminar boundary layer profile
Find:
[Difficulty: 3]
If it satisfies BCs; Evaluate */ and /
Solution:
The boundary layer equation is
u
y
2
U
u
y
2 2
U
u 0 0
The BCs are
At y = 0
At y =
du
dy
0 y
2 1
2
2
y for which u = U at y =
0
Problem 9.25
Given:
Data on wind tunnel and boundary layers
Find:
[Difficulty: 2]
Pressure change between points 1 and 2
Solution:
Basic
equations
(4.12)
p
2
V
2
g z const
Assumptions: 1) Steady flow 2) Incompressible 3) No friction outside boundary laye
Problem 9.67
Given:
[Difficulty: 3]
Laboratory wind tunnel has fixed walls. BL's are well represented by 1/7-power
profile. Information at two stations are known:
The given or available data (Table A.9) is
m
U1 26.1
s
Find:
H 305 mm W 305 mm 1 12.2 mm 2 1
Problem 9.81
Given:
Aircraft cruising at 12 km
Find:
[Difficulty: 3]
Skin friction drag force; Power required
Solution:
Basic
equations:
CD
FD
1
2
V A
2
We "unwrap" the cylinder to obtain an equivalent flat plate
L 38 m
From Table A.3, with
D 4 m
z 1200
Problem 10.24
[Difficulty: 3]
Given:
Data on suction pump
Find:
Plot of performance curves; Best effiiciency point
Solution:
p
Basic equations:
= 1.94 slug/ft
Ph
Ph Q g H
Pm
3
(Note: Software cannot render a dot!)
Fitting a 2nd order polynomial to each
Problem 10.33
[Difficulty: 3]
Given:
Data on a pump
Find:
Shutoff head; best efficiency; type of pump; flow rate, head, shutoff head and power at 900 rpm
Solution:
The given or available data is
999
3
kg
Ns 1.74
3
D 500 mm
Q 0.725
m
H 10 m
s
m
Wm 90 kW
Problem 10.39
[Difficulty: 3]
Given:
Data on Peerless Type 10AE12 pump at 1720 rpm
Find:
Data at speeds of 1000, 1200, 1400, and 1600 rpm
Solution:
Q1
The governing equations are the similarity rules:
1 D1
For scaling from speed 1 to speed 2:
Speed (rpm)
Problem 10.53
Given:
Pump and supply pipe system
Find:
[Difficulty: 3]
Maximum operational flow rate
Solution:
H
2
2
p
p
V1
V2
1
2
1
g z1
2
g z2 h lT
2
2
Basic equations:
h lT f
NPSHA
2
2
Le V2
LV
V
f
K
2
D2
D2
Le for the elbow, and K for th
Problem 10.61
Given:
Data on pump and pipe system
Find:
[Difficulty: 3]
Delivery through system, valve position to reduce delivery by half
Solution:
Governing Equations:
For the pump and system
where the total head loss is comprised of major and minor los
normalshock_25
Consider the flow of air through the converging-diverging nozzle shown in the figure below. The flow begins at
stagnation conditions with p0 = 100 kPa (abs) and T0 = 300 K. The nozzle exit-to-throat area ratio is AE/AT = 1.688
-4
2
with a t
Problem 2.1
Given:
Velocity fields
Find:
[Difficulty: 1]
Whether flows are 1, 2 or 3D, steady or unsteady.
Solution:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
V = V ( x , y)
V = V ( x , y)
V = V ( x)
V = V ( x)
V = V ( x)
V = V ( x , y)
V = V ( x , y)
V = V ( x , y
Problem 3.54
Given:
Gate geometry
Find:
[Difficulty: 3]
Depth H at which gate tips
Solution:
This is a problem with atmospheric pressure on both sides of the plate, so we can first determine the location of the
center of pressure with respect to the free
Problem *3.94
[Difficulty: 2]
Given:
Experiment performed by Archimedes to identify the material conent of King
Hiero's crown. The crown was weighed in air and in water.
Find:
Expression for the specific gravity of the crown as a function of the weights i
Problem 4.13
[Difficulty: 3]
Given:
Data on velocity field and control volume geometry
Find:
Volume flow rate and momentum flux
z
Solution:
3m
First we define the area and velocity vectors
y
r
dA = dydzi + dydyxk
r
V = axi + by
j
4m
5m
r
V = xi + y
j
or
x
Problem 4.33
Given:
Data on flow down an inclined plane
Find:
[Difficulty: 2]
Find u max
Solution:
Basic equation
mflow = u dA
Assumptions: 1) Steady flow 2) Incompressible flow
h
0
Evaluating at 1 and 2
h
0
2
2
g sin ( ) w
g sin ( )
y
mflow =
h y
Problem 4.35
Given:
Data on flow at inlet and outlet of pipe
Find:
[Difficulty: 2]
Find U
Solution:
Basic equation
r
r
V dA = 0
CS
Assumptions: 1) Steady flow 2) Incompressible flow
Evaluating at inlet and exit
2
U R +
R
u ( r) 2 r dr = 0
0
u max R
2