ME 311 Semester 121
Mechanical Engineering DepartmentKFUPM
HW # 2
Date Assigned: Sep. 15, 2012
Due Date: Sep. 22, 2012
1) Solve Problem # 3.3 in Textbook
2) Determine the gage pressure (in psig) at
point a; as shown in the figure, if liquid A has a
SG=0
4.4: PROBLEM DEFINITION
Situation:
For pathlines, streaklines, and streamlines to all be colinear, the ow must be
a) dividing
b) stagnant
c) steady
d) a tracer
SOLUTION
The answer is (c) steady.
4
4.35: PROBLEM DEFINITION
Situation:
Flow through an incli
Crowe/Engineering Fluid Mechanics
3.4: PROBLEM DEFINITION
Situation:
A Crosby gage tester is applied to calibrate a pressure gage.
Indicated pressure on the gage is p = 200 kPa.
W = 140 N, D = 0.03 m.
Find:
Percent error in gage reading.
PLAN
1. Calculate
Crowe/Engineering Fluid Mechanics
3.62: PROBLEM DEFINITION
Situation:
A submerged gate sits at an angle.
h = 6 m, b = 4 m, = 30 .
Find:
Reaction at point A.
Assumptions:
Gate is weightless.
Properties:
Water, Table A.5: = 9810 N / m3 .
PLAN
The reaction a
Crowe/Engineering Fluid Mechanics
4.11: PROBLEM DEFINITION
Situation:
Dye is injected into a ow eld and produces a streakline.
Pathline starts at t = 4 s, ends at t = 10 s . Flow speed is constant.
Find:
Draw a pathline of the particle.
SOLUTION
The strea
4.38: PROBLEM DEFINITION
Situation:
A piston and water accelerating upward at 0.4g.
a = 0.4g, z = 0.6 m.
Find:
Pressure in water column (Pa).
Properties:
= 1000 kg/ m3 , = 9810 N/ m3
PLAN
Apply Eulers equation.
SOLUTION
Eulers equation
a =
Let
(p + z)
b
Crowe/Engineering Fluid Mechanics
3.51: PROBLEM DEFINITION
Situation:
A force due to pressure is acting on an airplane window.
Window is at & elliptical. a = 0.3 m, b = 0.2 m .
pinside = 100 kPa, z = 10 km .
Find:
Outward force on the window (in N).
PLAN
Crowe/Engineering Fluid Mechanics
4.42: PROBLEM DEFINITION
Situation:
A tank of liquid is rotated on an arm.
S = 0.80, D = 30 cm.
h = 30 cm, r = 60 cm.
VA = 6 m/s, pA = 1200 Pa.
Find:
Pressure at B (Pa).
Properties:
= 1000 kg/ m3 , = 9800 N / m3 .
PLAN
A
Crowe/Engineering Fluid Mechanics
4.24: PROBLEM DEFINITION
Situation:
Water ow in a nozzle.
V = 2t/ 1 (0.5x/L)2 , L = 2 m, x = 0.5L, t = 3 s.
Find:
Local acceleration (m / s2 ).
Convective acceleration (m / s2 ).
SOLUTION
a
V
t
2t
=
t 1 (0.5x/L)2
2
=
1 (0
3.15: PROBLEM DEFINITION
Situation:
A closed tank contains air, oil, and water.
Find:
Specic gravity of oil.
Pressure at C (kPagage).
Sketch:
Properties:
Water (10 C), Table A.5, = 9810 N/ m3 .
PLAN
1.
2.
3.
4.
Find the oil specic gravity by applying the
5.9: PROBLEM DEFINITION
Situation:
Water ows in a pipe.
V = 4 m/ s, D = 2 m.
Find:
Discharge in m3 /s.
PLAN
Apply the ow rate equation.
SOLUTION
Flow rate equation
Q = VA
(2 m)2
4
Q = 12.6 m3 /s
= (4 m/ s)
9
5.78: PROBLEM DEFINITION
Situation:
A tire deve
Crowe/Engineering Fluid Mechanics
5.10: PROBLEM DEFINITION
Situation:
A duct is attached to an aircraft engine.
m = 200 kg / s, V = 240 m / s.
Find:
Pipe diameter (m).
Properties:
Air (18 C, 50 kPa) Table A.2: R = 287 J / kg K.
p = 50 kPa.
PLAN
1. Apply t
Crowe/Engineering Fluid Mechanics
6.16: PROBLEM DEFINITION
Situation:
Free water jet from upper tank to lower tank, lower tank supported by scales A
and B.
Q = 0.05 m3 / s, d1 = 0.1 m.
h = 0.3 m, H = 3 m
WT = 1 kN, A2 = 0.5 m2 .
Find:
Force on scale A (N)
6.7: PROBLEM DEFINITION
Situation:
A balloon is held stationary by a force.
d = 1 cm, p = 20 cm H2 O.
Find:
xcomponent of force required to hold balloon stationary (N).
Exit velocity (m/s).
Sketch:
Assumptions:
Steady, irrotational, constant density ow.
Crowe/Engineering Fluid Mechanics
7.24: PROBLEM DEFINITION
Situation:
Water is pushed out a nozzle by a pump.
Q = 0.1 m3 / s, D2 = 30 cm.
Dn = 10 cm, zn = 7 m .
z1 = 1 m, z2 = 2 m.
Find:
Pressure head at point 2.
SOLUTION
Flow rate equation to nd Vn (velo
Crowe/Engineering Fluid Mechanics
8.11: PROBLEM DEFINITION
Situation:
Vortex meter for ow rate measurement.
Find:
The functional relation in the form
Q
= f ( 1 , 2 )
D3
PLAN The functional form of the equation is
Q = (, D, l, , )
Use the stepbystep meth
Crowe/Engineering Fluid Mechanics
6.8: PROBLEM DEFINITION
Situation:
Water jet is lling a tank.
m = 12 kg, V = 20 liters.
d = 0.05 m, v = 15 m/s.
Find:
Minimum coecient of friction so force on stop block is zero.
Assumptions:
Steady ow, constant density,
Crowe/Engineering Fluid Mechanics
3.18: PROBLEM DEFINITION
Situation:
A tank is tted with a manometer.
S = 3, z1 = 0.15 m .
Find:
Deection of the manometer (cm).
Properties:
water =9810 N/m3 .
PLAN
Apply the hydrostatic principle to the water and then to
2.36
Situation:
Laminar ow occurs between two horizontal parallel plates. The velocity distribution is
y
1 dp
Hy y 2 + ut
u=
2 ds
H
Pressure p decreases with distance s, and the speed of the upper plate is ut . Note
that ut has a negative value to represe
Crowe/Engineering Fluid Mechanics
2.19: PROBLEM DEFINITION
Situation:
Air at certain temperatures.
T1 = 10 C, T2 = 70 C.
Find:
Change in kinematic viscosity.
Properties:
From Table A.3, 70 = 1.99 105 m2 /s, 10 = 1.41 105 m2 /s.
PLAN
Use properties found i
ME 311. Semester 121
Mechanical Engineering Department. KFUPM
Home Work # 3
Date Assigned: Sep. 22, 2012
Due Date: Sep. 29, 2012
1) Solve Problem # 3.75 from Textbook
2) Solve Problem # 3.77 from Textbook
3) Solve Problem # 3.85 from Textbook
4) The parab
ME 311 : Fluid Mechanics
Assignment # 4 (Semester 121)
Due Date: October 6th, 2012
1) Problem # 4.12 in Textbook
2) Problem # 4.24 in Textbook
3) Problem # 4.36 in Textbook
4) The figure below shows an elevation view of a centrifugal pump impeller of oute
Homework # 4
Text book: 4.19, 4.52, 4.92
Problem 1A water pipe bursts as a result of freezing, and water shoots up into the air a
certain height. The gage pressure of water in the pipe is to be determined.
Problem 2
Air is flowing through a venturi meter
ME 311 : Fluid Mechanics
Solution of HW # 4
1) Problem # 4.12 in Textbook
Data: A hypothetical flow has the following characteristics:
For 0 t 5 seconds, u = 2 m/s, v = 0
For 5 < t 10 seconds, u = 3 m/s, v = 4 m/s
At t=0 a dye streak was started, and a pa
ME311, Semester 121
Mechanical Engineering Department. KFUPM
Home Work # 6
Date Assigned: Nov. 3, 2012
Due Date: Nov. 10, 2012
Problem # 5.18
Problem # 5.61
Problem # 5.104
Problem # S1
A tank is being filled with water from a pipe as
shown. The volume f
ME311, Semester 121
Mechanical Engineering Department. KFUPM
Solution of Home Work # 6
Date Assigned: Nov. 3, 2012
Due Date: Nov. 10, 2012
Problem # 5.18
Q = u dA
A
cos(30)
= 1.5
y
1
3
dy
0
3
= 1.5 y
4
4
cos(30)
3
0
Q = 0.93(m 3 s )
Problem # 5.61
To fin
lillTater
Armb‘sfs This problem involves the conversion of ﬂow. kinetic. and potential energies to each other
without involving any pumps. turbines. and wasteful components with large frictional losses. and thus it is
suitable for the use of the Bernoul
ME 311. Semester 121
Mechanical Engineering Department. KFUPM
HW # 8 Due Date: Dec 1st (2pm), 2012
Problems 1, 2 and 3: Solve Problems: 7.35, 7.50, 7.83 from Textbook
P4. The total losses in the siphon shown below are estimated to be hLt=4V2/2g. The loss
ME 311 Semester 121

Mechanical Engineering DepartmentKFUPM
HW # 7
Date Assigned: Nov 10th , 2012
Due Date: Nov 24 th , 2012
From the textbook:
1. Problem # 6.12
2. Problem # 6.20
3. Problem # 6.44
The circular dish, whose cross section is shown
, has a
ME 311 : Fluid Mechanics
Assignment # 9 (Semester 121)
Due Date: December 8th, 2012
1) Problem # 8.9 in Textbook
F
f (1 , 2 , 3 )
Erratum :
2 2
Vo D
2) Problem # 8.47 in Textbook
3) Problem # 8.64 in Textbook
4) A model test is performed to study flow
MIMEVersion: 1.0
ContentType: multipart/related; boundary="=_NextPart_01CD9FF3.236E1A60"
This document is a Single File Web Page, also known as a Web Archive file. If
you are seeing this message, your browser or editor doesn't support Web Archive
files
Example Problem for Moment of Momentum Principle
For the figure below of a garden sprinkler, a) find the torque T such that = 0, b) find
, if torque T = 0.
Solution:
The first step is to select the Control Volume. This is shown below.
We use the a fixed c
Qs. Find dp dx at x = 0.5L as
shown in the figure, if
V = cfw_10 + 40x i (m/s).
G
Solution: Since V = u i + v j + w k ,
therefore,
u = 10 + 40x and v = w = 0 .
The Euler's equation is given as,
G
G
G
G
V
V
V
V
1 G
+u
+v
+w
= ( p + z )
t
x
y
z
G
G
G
V
V
V
3.4 Hydrostatic Forces on Plane Surfaces
If a plane surface immersed in a fluid is
horizontal, then
Hydrostatic pressure is uniform over the
entire surface.
The resultant force acts at the centroid of
the plane.
F
If a plane surface immersed in a flui
Solution:
= 45 , y =
l 4
l
+ = 0.854 l , A = l w
sin(45) 2
PlaneGate
FR = y sin( )A ;
FR = ( 0.854 l ) sin(45) ( l w )
FR = 0.604 l 2w
y CP = y +
I
wl 3 12
l 12
= 0.854l +
= 0.854l +
= 0.952l
yA
0.854l lw
0.854
TofindthereactionatpointAwesummomentsa