BIEN 301
Individual Project Presentation
Hydrostatic Force Against A
Dam
Scott C. Laura
Hydrostatic Force:
• The pressure force related to the
weight of a fluid bearing on a
surface
• No motion in the fluid
• Sum of forces = zero
Need to Know Values
Horizontal Component, Fh
The horizontal component of force on a curved
surface equals the force on the plane area formed
by the projection of the curved surface onto a
vertical plane normal to the component.
Δx
The force in the x
direction can be
thought of as a
resistance to shear
stress
F  h A
h
cg proj
Fh has a line of action below the centroid (0,0)
onto the point ycp
 xx
 I  si n
y
cp  proj

h A
cg

proj
Actually
Z
Z
Add Mag
Below
of Ycp = The
To ½ Z
Surface
X
Y
Vertical Component, Fv
The vertical component of force on a curved
surface equals the weight of the effective
column of fluid necessary to cause the
pressure on the surface.
Δz
+ Patm
Force at any point
is equal to the sum
of all the above
weights
F   A
v
b
section
The force acts downward through the
centroid
Problem # 2.82
Determine the horizontal and vertical components
of the hydrostatic force against the dam and the
point (CP) where the resultant strikes the dam.
Fig. P2.82
20 m
Pa = 0
20 m
CP
Water
50 m
Assumptions:
1. Hydrostatic – water
is not moving
2. Uniform Density
3. Incompressible
4. 20 degrees
Given:
•
•
•
•
•
H = 20 meters
L = 20 meters
W = 50 meters
pa = 0
Quarter Circle
in shape
Water
Dam
Approach:
Hydrostatic Forces On Curved Surfaces
1.
2.
3.
4.
5.
Calculate Fh
Calculate Ycp
Calculate Fv
Calculate the x value of the centroid
Find the resultant force
N

h
9 79 0
3
m
cg
A
proj
1 0m
2 0m 5 0m
F
h
9 79 01
 0 2 0 5 0 9 7.9MN
 xx
 I  si n
y
cp  proj

h A
cg
y
cp  proj

proj
1 
3



 5 0m 2 0 

 1 2 

1 0m 2 0m 5 0m
3 .33 3m
F   A
v
F
v
b
section
2

N   ( 2 0 m) 
9 79 0

 5 0m 1 53 .8MN
3
m
4
x
( 4 2 0m)
3
8 .5m
Resultant:
F
F
 F 2  F 2
  h  v 
 1
 
 2
 ( 9 7.9MN) 2  ( 1 53 .8MN) 2
Tan-1(153.8/97.9) = 57.5°
 1
 
 2
1 82 .3MN
ө
BME Application
Hydrostatic force is a vital concept in estimating our
body’s conditions
From headaches to keeping us alive through diffusion and
osmosis
Our body can even sense when we need to urinate by the
pressure within the bladder