1. Forces due to Static Fluids
Pressure =Force/Area (definition)
Force = Pressure*Area
Example:
If a cylinder has an internal diameter of 50 mm and operates at a pressure of 20 bar, calculate the force on the ends of the cylinder.

2. Example: Cylinder Calculate the force on the bottom of the container.
Oil, S.G. = 0.90
1.5 m
Water, S.G. =1.0

3. Example: Cone Shaped Container
Calculate the force on the
bottom of the container.
2.4 m
Oil, S.G. = 0.90
1.5 m
Water, S.G. =1.0
3 m

4. Force-Pressure: Rectangular Walls
Patm
Vertical wall
DP = g*h d

5. Derivation of Resultant Force (FR) on a rectangular (vertical) wall
FR = g*(d/2)*A = Pavg*A
Pavg = g*(d/2)
LP = d/3
Patm
DP = g*h d FR
Center of Pressure (CP)
d/3

6. Procedure for computing the resultant force on a rectangular (vertical) wall
Calculate the magnitude of FR
FR = g*(d/2)*A = Pavg*A; Pavg = g*(d/2)
Locate center of pressure at a vertical distance d/3 from the bottom of the wall (comes from sums of forces and moments, SF = 0; SM = 0)
Show the resultant force acting at the center of pressure perpendicular to the wall

7. Example
Fluid is gasoline (S.G. = 0.68) and the total depth is 30 m. The wall is 12 m long. Calculate the magnitude of the resultant force on the wall and the location of the center of pressure.

8. Example
A dam, 30.5 m long, which retains 8 m of water and is inclined at an angle of 60°. Calculate the magnitude of the resultant force on the dam and the location of the center of pressure.
60°
d = 8 m

9. Submerged Plane Areas Definitions FR: Resultant Force
CP: Center of Pressure
CT: Centroid of the area
- q: Angle of inclination
hc: Depth of fluid from free surface
Lc: Distance from free surface to centroid of area
Lp: Distance from free surface to center of pressure
B, H: Dimensions of area

10. Procedure for computing FR on a submerged plane area
Identify the point S, where inclined plane intersects free surface
Locate the centroid of the interested area
Determine hC
Determine LC, hc = Lcsinq
Calculate A, area of interest, A = BH
Calculate FR, FR = ghcA
Calculate IC, Moment of Inertia, Ic = BH3/12

11. Procedure for computing FR on a submerged plane area
Determine LP; LP = LC + IC/LCA, comes from SF and SM
Show FR, LP, LC
Compute and show hp, hp = Lpsinq

12. Example
Lubricating oil with a S.G. of The rectangular gate with the following dimensions B = 2m and H = 0.5 m is placed in the inclined wall of the tank (q = 60°). The centroid of the gate is at a depth of 1.5 m from the surface. Calculate FR and LP.

13. Piezometric Head hA
hA = PA/g
hAC = hA + hC
hAC hC

14. Example
Consider previous example, except the tank is sealed at the top and the pressure is 10 k.Pa gauge above the oil.

15. Forces on Curved Surfacesh1 h2

16. Submerged Curved Surface
Resultant force can be broken up into horizontal and vertical components or vectors
Horizontal component:
FH = g*s*w*(h + s/2),
Where,
h = Depth to the top of rectangle (beginning of curve surface)
s = projected rectangle height
w = projected rectangle length or width
Center of pressure
hp = hC + IC/(hCA)
hC = h + s/2
hp = hC + s2/(12hC)

17. Submerged Curved Surface
Vertical Component
FV = g*Volume = g*A*w
Where,
A = entire area of fluid
w = projected rectangle length or width
Location of centroid
Resultant Force

18. Procedure for computing the Force on Submerged Curved Surface
Isolate the volume of fluid above the surface
Compute the weight of the isolated volume
Compute the vertical component of force and its centroid
Draw a projection of the curved surface onto a vertical plane and determine its height, s.

19. Procedure for computing the Force on Submerged Curved Surface
Compute the depth to the centroid of the projected area, hc
Compute the horizontal component
Compute the depth to the line of action (center of pressure, hp)
Compute the resultant force
Compute the angle of inclination
Show or draw vector on diagram

20. Example
Compute the horizontal and vertical components, and resultant force on the curve surface
h1 = 3.00 m
h2 = 4.50 m
w = 2.50 m
g = 9.81 kN/m3 h1 h2