The plane region A is submerged in a fluid of weight density γ . The resultant force of the fluid pressure on the region is R acting at the point C (called the pressure center) located at the distance h below the surface of the fluid. Show that R = γ Q a and h = I a / Q a , where Q a and I a are the first and second moments of A about the axis a - a .
The plane region A is submerged in a fluid of weight density γ . The resultant force of the fluid pressure on the region is R acting at the point C (called the pressure center) located at the distance h below the surface of the fluid. Show that R = γ Q a and h = I a / Q a , where Q a and I a are the first and second moments of A about the axis a - a .
Solution Summary: The author explains that R=gamma Q_a and h=
The plane region A is submerged in a fluid of weight density
γ
.
The resultant force of the fluid pressure on the region is R acting at the point C (called the pressure center) located at the distance h below the surface of the fluid. Show that
R
=
γ
Q
a
and
h
=
I
a
/
Q
a
,
where
Q
a
and
I
a
are the first and second moments of A about the axis a-a.
3. An engine has three cylinders spaced at 120° to each other. The crank torque diagram can be simplified to a
triangle having the following values:
Angle
0°
Torque (Nm)
0
(a) What is the mean torque?
60°
4500
180°
180° to 360°
0
0
(b) What moment of inertia of flywheel is required to keep the speed to within 180 ± 3 rpm?
(c) If one cylinder of the engine is made inoperative and it is assumed that the torque for this cylinder is
zero for all crank angles, determine the fluctuation in speed at 180rpm for the same flywheel.
(a) 3375 Nm
(b) 50kgm
(c) ±21 rpm
Prob 5.
Determine the largest load P that can be applied to
the frame without causing either the average
normal stress or the average shear stress at section
a-a to exceed o-150 MPa and 1-60 MPa,
respectively.
Member CB has a square cross section of 25 mm
on each side.
2 m
FAC
1.5 m
Fac
Derive the component transformation equations for tensors shown below where [C] = [BA] is the DCM (direction cosine matrix) from frame A to B.
^B [T] = [C]^A [T] [C]^T
Chapter 9 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
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