Problem 3.82
[Difficulty: 3]
Given:
Curved surface, in shape of quarter cylinder, with given radius R and width w; water stands to depth H.
R
0.750 m
⋅
=
w
3.55 m
⋅
=
H
0.650 m
⋅
=
Find:
Magnitude and line of action of (a) vertical force and (b) horizontal force on the curved
surface
Solution:
We will apply the hydrostatics equations to this system.
Governing Equations:
dp
dh
ρ
g
⋅
=
(Hydrostatic Pressure  h is positive downwards from
free surface)
F
v
A
y
p
⌠
⎮
⎮
⌡
d
=
(Vertical Hydrostatic Force)
F
H
p
c
A
⋅
=
(Horizontal Hydrostatic Force)
x' F
v
⋅
F
v
x
⌠
⎮
⎮
⌡
d
=
(Moment of vertical force)
h'
h
c
I
xx
h
c
A
⋅
+
=
(Line of action of horizontal force)
dF
h
H
R
θ
Assumptions:
(1) Static fluid
(2) Incompressible fluid
(3) Atmospheric pressure acts on free surface of the
water and on the left side of the curved surface
Integrating the hydrostatic pressure equation:
p
ρ
g
⋅
h
⋅
=
dF
h’
H
R
F
V
F
H
y’
x’
From the geometry:
h
H
R sin
θ
()
⋅
−
=
y
R sin
θ
⋅
=
x
R cos
θ
⋅
=
dA
w R
⋅
d
θ
⋅
=
θ
1
asin
H
R
⎛
⎝
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 Lear
 Fluid Mechanics

Click to edit the document details