Fluid statics II
CHEE 3363 Spring 2014 Handout 6
�Reading: Fox 3.5
�1
Learning objectives for lecture
1. Calculate the force on a submerged surface.�
2. Calculate the moment on a submerged surface about a given point.
�2
Hydrostatic force on submerged surfaces 1
θh
dF
Recall:forces normal to the surface
y
Hydrostatic force on submerged surfaces 2
θh
dF
y
Evaluate resultant force FR
Hydrostatic force on submerged surfaces 3
θh
dF
y
To calculate the location (x′ y′ FR �
y′,
�5
h = y sin θ, H = L sin θ
Hydrostatic force on submerged surface
H
yInclined Plate,width w
O
h
x
Force
Moment
�6
1
a distance h0
�7
x
y
Inclined Plate,width w. length L
O
h h0
A
B
Moment on submerged plate about point A
a distance h0
�8
x
y
Inclined Plate,width w. length L
O
h h0
A
B
Moment on submerged plate about point A
�9
x
y
Inclined Plate,width w. length L
O
h h0
A
B
Moment on submerged plate about point Bx
y
Inclined Plate,width w. length L
O
h h0
A
B
a distance h0
�10
Moment on submerged plate about point Bx
y
Inclined Plate,width w. length L
O
h h0
A
B
�11
Forces on curved planes 1
Magnitude of force in an arbitrary direction l:
�12
Forces on curved planes 2
�13
Horizontal force:
Vertical force:
1
RH
x
y
x
Force FR
x-component of force F
2
RH
x
y
x
�15
y-component of force F
Magnitude of force FR
1
�17
Givenρ.�
Find
Evaluate FR
2
�18
Givenρ.�
Find
Evaluate y′FR
1
�19
Given D and length L �1 h1 and �
SG2 h2.�Find
F and F
2
�20
Given D and length L �1 h1 and �
SG2 h2.�FindEvaluate pressures on each side as a function of θ
Final integrals for F and F
F =
∫
A
pdA
Fn = n · F =
∫
A
p dAn dAn = n·dA
Component of the force in the direction n
To calculate the location (x′ y′
y′=
y′F
F=
∫A
yp dA∫A
p dA
∑M0 = 0, M0 =
∫
A
RpdA R = distance to axis of rotation�21