BIEN 301Individual 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.

The force in the x direction can be thought of as a resistance to shear stress

Δx

Fh

hcg

Aproj

proj

ycp proj

Ixx

sin

hcg

Aproj

cg

Fh has a line of action below the centroid (0,0) onto the point ycp

Actually Z

Z

X

Y

Add Mag of YcpTo ½ Z

=BelowTheSurface

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.

+ Patm

Force at any point is equal to the sum of all the aboveweights

Δz

Fv

Asection

b b

The force acts downward through the centroid

Problem # 2.82Determine the horizontal and vertical components

of the hydrostatic force against the dam and the point (CP) where the resultant strikes the dam.

Water

20 m

20 m

CP

Pa = 0

50 m

Fig. P2.82

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. Calculate Fh

2. Calculate Ycp

3. Calculate Fv

4. Calculate the x value of the centroid

5. Find the resultant force

9790N

m3

Fh

979010 20 50 97.9MNh

cg10m

Aproj

20m 50 m

ycp proj

Ixx

sin

hcg

Aproj

cg

ycp proj

1

12

50 m 203

10m 20 m 50 m3.333 m

Fv

Asection

b b

Fv

9790N

m3

20 m( )

2 4

50 m 153.8MN

x4 20 m( )

38.5m

F Fh 2 F

v 2

1

2

F 97.9MN( )2

153.8MN( )2

1

2

182.3MN

Resultant:

Tan-1(153.8/97.9) = 57.5°

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