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

3

RH

x

y

x

�16

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