Fluid Mechanics (2nd Edition)
2nd Edition
ISBN: 9780134649290
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 7, Problem 43P
To determine
Whether the flow is rotational or irrotational, and the pressure at the origin .
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2. Express the following complex numbers in rectangular form.
(a) z₁ = 2еjл/6
(b) Z2=-3e-jπ/4
(c) Z3 =
√√√3e-j³/4
(d) z4 = − j³
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…
Chapter 7 Solutions
Fluid Mechanics (2nd Edition)
Ch. 7 - Prob. 1PCh. 7 - A flow is defined by its velocity components u =...Ch. 7 - A uniform flow at 6 m/s is directed at an angle of...Ch. 7 - Prob. 4PCh. 7 - Prob. 5PCh. 7 - Determine the stream and potential functions for...Ch. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - Prob. 9PCh. 7 - The velocity profile of a liquid flowing along the...
Ch. 7 - Prob. 11PCh. 7 - Prob. 12PCh. 7 - The liquid confined between two moving plates has...Ch. 7 - Prob. 14PCh. 7 - Prob. 15PCh. 7 - Prob. 16PCh. 7 - A flow has velocity components u = 2(y − x) ft/s...Ch. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - Prob. 24PCh. 7 - Prob. 25PCh. 7 - Prob. 26PCh. 7 - Prob. 27PCh. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Prob. 30PCh. 7 - Prob. 31PCh. 7 - Prob. 32PCh. 7 - Prob. 33PCh. 7 - Prob. 34PCh. 7 - Prob. 35PCh. 7 - Prob. 36PCh. 7 - Prob. 37PCh. 7 - Prob. 38PCh. 7 - Prob. 39PCh. 7 - Prob. 40PCh. 7 - Prob. 41PCh. 7 - Prob. 42PCh. 7 - Prob. 43PCh. 7 - If a building has a flat roof and is located 20 m...Ch. 7 - Prob. 45PCh. 7 - Combine a source of strength q with a free...Ch. 7 - Prob. 47PCh. 7 - Show that the equation that defines a sink will...Ch. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - Prob. 52PCh. 7 - Prob. 53PCh. 7 - Prob. 54PCh. 7 - Prob. 55PCh. 7 - A source q is emitted from the wall while a flow...Ch. 7 - Prob. 57PCh. 7 - Prob. 58PCh. 7 - Prob. 59PCh. 7 - Prob. 60PCh. 7 - Prob. 61PCh. 7 - Prob. 62PCh. 7 - Prob. 63PCh. 7 - Prob. 64PCh. 7 - Prob. 65PCh. 7 - The long rotating cylinder is subjected to a...Ch. 7 - Prob. 67PCh. 7 - Prob. 68PCh. 7 - Prob. 69PCh. 7 - Prob. 70PCh. 7 - Prob. 71PCh. 7 - Prob. 72PCh. 7 - Prob. 73PCh. 7 - Prob. 74PCh. 7 - Prob. 75PCh. 7 - Prob. 76PCh. 7 - Prob. 77PCh. 7 - Prob. 78PCh. 7 - If the uniform velocity of the air is 15 m/s and...Ch. 7 - Prob. 80PCh. 7 - The long cylinder is rotating counterclockwise...Ch. 7 - Prob. 82PCh. 7 - Liquid is confined between a top plate having an...Ch. 7 - A horizontal velocity is defined by u = 2(x2 − y2)...Ch. 7 - The sloped open channel has steady laminar flow...Ch. 7 - Prob. 86PCh. 7 - The channel for a liquid is formed by two fixed...
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