Fluid Mechanics Fundamentals And Applications
3rd Edition
ISBN: 9780073380322
Author: Yunus Cengel, John Cimbala
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 8, Problem 105CP
To determine
The difference between the principles of operation of thermal and laser Doppler anemometers.
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A prismatic beam is built into a structure. You can consider the boundary conditions at A and B to be
fixed supports. The beam was originally designed to withstand a triangular distributed load, however,
the loading condition has been revised and can be approximated by a cosine function as shown in the
figure below. You have been tasked with analysing the structure. As the beam is prismatic, you can
assume that the bending rigidity (El) is constant.
wwo cos
2L
x
A
B
Figure 3: Built in beam with a varying distributed load
In order to do this, you will:
a. Solve the reaction forces and moments at point A and B.
Hint: you may find it convenient to use the principal of superposition.
(2%)
b. Plot the shear force and bending moment diagrams and identify the maximum shear force
and bending moment.
(2%)
c. Develop an expression for the vertical deflection. Clearly state your expression in terms of x.
(1%)
Question 1: Beam Analysis
Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts
as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces
can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a
roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied
to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB
and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these
moments is PL.
Moment Release
A
B
с
°
MB = PL
Mc=
= PL
-L/2-
-L/2-
→
P
D
Figure 1: Two beam arrangement for question 1.
To analyse this structure, you will:
a) Construct the free body diagrams for the structure shown above. When constructing your
FBD's you must make section cuts at point B and C. You can represent the structure as three
separate beams. Following this, construct the…
A cantilevered rectangular prismatic beam has three loads applied. 10,000N in the positive x
direction, 500N in the positive z direction and 750 in the negative y direction. You have been tasked
with analysing the stresses at three points on the beam, a, b and c.
32mm
60mm
24mm
180mm
15mm
15mm
40mm
750N
16mm
500N
x
10,000N
Figure 2: Idealisation of the structure and the applied loading (right). Photograph of the new product
(left). Picture sourced from amazon.com.au.
To assess the design, you will:
a) Determine state of stress at all points (a, b and c). These points are located on the exterior
surface of the beam. Point a is located along the centreline of the beam, point b is 15mm
from the centreline and point c is located on the edge of the beam. When calculating the
stresses you must consider the stresses due to bending and transverse shear. Present your
results in a table and ensure that your sign convention is clearly shown (and applied
consistently!)
(3%)
b) You have identified…
Chapter 8 Solutions
Fluid Mechanics Fundamentals And Applications
Ch. 8 - Consider the flow of air and wale in pipes of the...Ch. 8 - Consider laminar flow in a circular pipe. Is the...Ch. 8 - What is hydraulic diameter? How is it defined?...Ch. 8 - How is the hydrodynamic entry length defined for...Ch. 8 - Why are liquids usually transported in circular...Ch. 8 - What is the physical significance of the Reynolds...Ch. 8 - Consider a person walking first in air and then in...Ch. 8 - Show that the Reynolds number for flow in a...Ch. 8 - Which fluid at room temperature requires a larger...Ch. 8 - What is the eneia1Iy accepted value of the...
Ch. 8 - How does surface roughness affect the pressure...Ch. 8 - Shown here is a cool picture of water being...Ch. 8 - Someone claims that the volume flow rate in a...Ch. 8 - Someone claims that the average velocity in a...Ch. 8 - Someone claims that the shear stress at the center...Ch. 8 - Someone claims that in fully developed turbulent...Ch. 8 - How does the wall shear stress w , vary along the...Ch. 8 - What fluid property is responsible for the...Ch. 8 - In the fully developed region of flow in a...Ch. 8 - How is the friction factor for flow in a pipe...Ch. 8 - Discuss whether fully developed pipe flow is one-,...Ch. 8 - Consider fully developed flow in a circular pipe...Ch. 8 - Consider fully developed laminar how in a...Ch. 8 - Explain why the friction factor is independent of...Ch. 8 - What is turbulent viscosity? What caused it?Ch. 8 - The head toss for a certain circular pipe is given...Ch. 8 - Consider fully developed laminar flow in a...Ch. 8 - How is head loss related to pressure loss? For a...Ch. 8 - Consider laminar flow of air in a circular pipe...Ch. 8 - What is the physical mechanism that causes the...Ch. 8 - The velocity profile for the fully developed...Ch. 8 - Prob. 32PCh. 8 - Water at 10°C ( =999.7kg/m3 and =1.307103kg/ms )...Ch. 8 - Consider an air solar collector that is 1 m wide...Ch. 8 - Heated air at 1 atm and 100F is to be transported...Ch. 8 - In fully developed laminar flow in a circular...Ch. 8 - The velocity profile in fully developed laminar...Ch. 8 - Repeat Prob. 8-36 for a pipe of inner radius 7 cm.Ch. 8 - Water at 15°C (p = 999.1 kg/m3 and = 1.138 × 10-3...Ch. 8 - Prob. 40PCh. 8 - Consider laminar flow of a fluid through a square...Ch. 8 - Repeat Prob. 8-39 for tribulent flow in smooth...Ch. 8 - Prob. 43PCh. 8 - Water at 70F passes through...Ch. 8 - Oil with p = 876 kg/m3 and = 0.24 kg/m.s is...Ch. 8 - Glycenii at 40 C with p = l22 kg/m3 and = 0.27...Ch. 8 - Air at 1 atm and 60 F is flowing through a 1 ft ×...Ch. 8 - Water enters into a cone of height H and base...Ch. 8 - The velocity profile for incompressible turbulent...Ch. 8 - Oil with a density of 850 kg/m3 and kinematic...Ch. 8 - In an air heating system, heated air at 40 C and...Ch. 8 - Glycerin at 40 C with p = 1252 kg/m3 and = 0.27...Ch. 8 - Oil at 80°F ( =56.8lbm/ft3 and =0.0278lbm/fts ) is...Ch. 8 - Liquid ammonia at 20 C is flowing through a...Ch. 8 - During a retrofitting project of a fluid flow...Ch. 8 - Define equivalent length for minor loss in pipe...Ch. 8 - The effect of rounding of a pipe inlet on the loss...Ch. 8 - The effect of rounding of a pipe exit on the loss...Ch. 8 - Which has a greater minor loss coefficient during...Ch. 8 - A piping system involves sharp turns, and thus...Ch. 8 - What is minor loss in pipe flow? How is the minor...Ch. 8 - Water is to be withdrawn from an 8-m-high water...Ch. 8 - Consider flow from a water reservoir through a...Ch. 8 - Repeat Prob. 8-62 for a slightly rounded entrance...Ch. 8 - A horizontal pipe has an abrupt expansion from...Ch. 8 - Water is pumped from a large lower reservoir to a...Ch. 8 - A piping system equipped with a pump is operating...Ch. 8 - Prob. 69CPCh. 8 - Consider two identical 2-m-high open tanks tilled...Ch. 8 - A piping system involves two pipes of different...Ch. 8 - A piping system involves two pipes of different...Ch. 8 - A piping system involves two pipes of identical...Ch. 8 - For a piping system, define the system curve, the...Ch. 8 - A 4-in-high cylindrical tank having a...Ch. 8 - Prob. 76PCh. 8 - The water needs of a small farm are to be met by...Ch. 8 - Prob. 78EPCh. 8 - A 2.4-m-diameter tank is initially filled with...Ch. 8 - A 3-m-diameter tank is initially filled with water...Ch. 8 - Reconsider Prob. 8-78. In order to drain the tank...Ch. 8 - Water to a residential area is transported at a...Ch. 8 - Prob. 83EPCh. 8 - Oil at 20 C is flowing through a vertical glass...Ch. 8 - Prob. 85PCh. 8 - Water at 15 C is drained from a large reservoir...Ch. 8 - A fanner is to pump water at 70 F from a river to...Ch. 8 - A water tank tilled with solar-heated vater at 4OC...Ch. 8 - Two water reservoirs A and B are connected to each...Ch. 8 - Prob. 91PCh. 8 - Prob. 92PCh. 8 - A certain pail of cast iron piping of a water...Ch. 8 - Repeat Prob. 8-91 assuming pipe A has a...Ch. 8 - Prob. 95PCh. 8 - Repeat Prob. 8-93 for cast lion pipes of the same...Ch. 8 - Water is transported by gravity through a...Ch. 8 - Water to a residential area is transported at a...Ch. 8 - Prob. 99PCh. 8 - Prob. 101PCh. 8 - A 6-m-tall chimney shown in Fig. P8103 is to be...Ch. 8 - Prob. 104PCh. 8 - Prob. 105CPCh. 8 - What is the difference between laser Doppler...Ch. 8 - What are the primary considerations when selecting...Ch. 8 - Prob. 108CPCh. 8 - Explain how flow rate is measured with...Ch. 8 - Prob. 110CPCh. 8 - Prob. 111CPCh. 8 - Prob. 112CPCh. 8 - The flow rate of water at 20°C (=998kg/m3) and...Ch. 8 - Prob. 114PCh. 8 - Prob. 115PCh. 8 - Prob. 116PCh. 8 - Prob. 117PCh. 8 - Prob. 118EPCh. 8 - Prob. 119EPCh. 8 - Prob. 120PCh. 8 - A Venturi meter equipped with a differential...Ch. 8 - Prob. 123PCh. 8 - Prob. 124PCh. 8 - Prob. 125PCh. 8 - Prob. 126EPCh. 8 - A 22-L kerosene tank (=820kg/m3) is filled with a...Ch. 8 - The flow rate of water at 20°C (p = 998 kg/m3 and ...Ch. 8 - Prob. 129PCh. 8 - Prob. 130PCh. 8 - The conical container with a thin horizontal tube...Ch. 8 - Shell-and-tube heat exchangers with hundred of...Ch. 8 - The compressed air requirements of a manufacturing...Ch. 8 - A house built on a riverside is to be cooled iii...Ch. 8 - The velocity profile in fully developed lamina,...Ch. 8 - Prob. 136EPCh. 8 - Repeat Prob. 8—136E assuming the pipe is inclined...Ch. 8 - Prob. 138PCh. 8 - Consider flow front a reservoir through a...Ch. 8 - Prob. 140PCh. 8 - A student is to determine the kinematic viscosity...Ch. 8 - A circular water pipe has an abrupt expansion from...Ch. 8 - Prob. 143PCh. 8 - Water at 15 C is to be dischaged froiti a...Ch. 8 - Two pipes of identical diameter and material are...Ch. 8 - A pipelme ihat Eransports oil ai 4OC at a iate of...Ch. 8 - Repeat Prob. 8-140 for hot-water flow of a...Ch. 8 - Prob. 149PCh. 8 - Prob. 152EPCh. 8 - Prob. 153EPCh. 8 - In a hydroelectric power plant. water at 20°C is...Ch. 8 - Prob. 155PCh. 8 - The water at 20 C in a l0-m-diameter, 2-m-high...Ch. 8 - Prob. 162PCh. 8 - Prob. 163PCh. 8 - Prob. 164PCh. 8 - Prob. 165PCh. 8 - Prob. 166PCh. 8 - Air at 1 atm and 20C flows in a 4-em-diameter...Ch. 8 - Consider laminar flow of water in a...Ch. 8 - Consider laminar flow of water at 15C in a...Ch. 8 - Engine oil at 40C(=876kg/m3,=0.2177kg/m.s) flows...Ch. 8 - A fluid flows in a 25-cm-diameter pipe at a...Ch. 8 - Watet flows in a I 5-cm-diameter pipe a, a...Ch. 8 - The pressure drop for a given flow is determined...Ch. 8 - Air at 1 atm and 25C(v=1.562X105m2/s) flows in a...Ch. 8 - Consider air flow in a 10-cm-diameter high...Ch. 8 - Air at 1 aim and 40 C flows in a 8-cm-diameter...Ch. 8 - Water at 10C(=999.7kg/m3,=1.307x103kg/m.s) is to...Ch. 8 - The valve in a piping system causes a 3.1 m head...Ch. 8 - Consider a sharp-edged pipe exit for fully...Ch. 8 - A water flow system involves a 180 return bend...Ch. 8 - A constant-diameter piping system involves...Ch. 8 - Air flows in an 8-cm-diameter, 33-m-long pipe at a...Ch. 8 - Consider a pipe that branches out into two...Ch. 8 - Prob. 184PCh. 8 - Prob. 185PCh. 8 - Prob. 186PCh. 8 - Prob. 187PCh. 8 - Design an experiment to measure the viscosity of...Ch. 8 - During a camping trip you notice that water is...
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