This document provides a training package on hydrostatic forces on plane surfaces for students in the Environmental Engineering Department. It includes an overview of the topic, objectives, examples, and pre-test and post-test questions. The key ideas covered are how hydrostatic forces form a system of parallel forces on submerged surfaces, how to calculate the magnitude and location of these forces on vertical, inclined, and curved surfaces, and examples demonstrating these calculations.

1. Ministry of Higher Education & Scientific Research
Foundation of Technical Education
Technical College of Basrah
CH.3: Hydrostatic Forces on Plane Surfaces
Training Package
in
Fluid Mechanics
Modular unit 3
Hydro static Force on Plane Surface
By
Risala A. Mohammed
M.Sc. Civil Engineering
Asst. Lect.
Environmental & Pollution Engineering Department
2011

2. 1- Over view
1-1 Target population
CH.3: Hydrostatic Forces on Plane Surfaces
For the students of second class in
Environmental engineering Department in
Technical College

3. 1-2 Rationale
CH.3: Hydrostatic Forces on Plane Surfaces
The study of force in fluid mechanics is very
important in applied field to calculate the amount of
force on the walls of the reservoirs, surfaces which
exposed to the effects of wind such as aircraft and high
buildings. In addition to the application in the field of
hydraulic structures to calculate the forces that
exposed on dams and gates.

4. 1-3 Central Idea
CH.3: Hydrostatic Forces on Plane Surfaces
The main goal of this chapter are:
1- Define the hydrostatic force.
2- Applied of the hydrostatic force on surface
plane .

5. 1-4 Instructions
CH.3: Hydrostatic Forces on Plane Surfaces
1- Study over view thoroughly
2- Identify the goal of this modular unit
3- Do the Pretest and if you :-
*Get 9 or more you do not need to proceed
*Get less than 9 you have to study this modular
4- After studying the text of this modular unit , do the post test
and if you :-
*Get 9 or more , so go on studying modular unit four
*Get less than 9 , go back and study the modular unit three

6. 1-5 Performance Objectives
CH.3: Hydrostatic Forces on Plane Surfaces
At the end of this modular unit the student will be able to :-
1- Define the hydrostatic force
2- calculate the magnitude and direction and it position of
hydrostatic pressure on vertical, inclined and curved
surfaces.

7. 2- Pre test
-
CH.3: Hydrostatic Forces on Plane Surfaces
Q1)) ( 5 mark)
The tank in Fig. below is 40cm wide. Compute
the hydrostatic forces on horizontal panels BE
and AD. Neglect atmospheric pressure .
Q2)) ( 5 mark)
the net hydrostatic force per unit width on
rectangular panel AB in Fig. below and
determine its line of action.
Not
Check your answers in key answer page

8. Hydrostatic Forces on Plane Surfaces
CH.3: Hydrostatic Forces on Plane Surfaces
 On a plane surface, the
hydrostatic forces form a
system of parallel forces
 For many applications,
magnitude and location of
application, which is called
center of pressure, must be
determined.
 Atmospheric pressure Patm can
be neglected when it acts on
both sides of the surface.

9. Hydrostatic Forces on Inclined Plane Surfaces
CH.3: Hydrostatic Forces on Plane Surfaces
The magnitude of FR acting on a plane surface of a completely submerged
plate in a homogenous fluid is equal to the product of the pressure PC at
the centroid of the surface and the area A of the surface

10. Hydrostatic Forces on Inclined Plane Surfaces
CH.3: Hydrostatic Forces on Plane Surfaces
Line of action of resultant force
FR=PCA does not pass through
the centroid of the surface. In
general, it lies underneath
where the pressure is higher.
 Vertical location of Center of
Pressure is determined by
equation the moment of the
resultant force to the moment of
the distributed pressure force.
,
xx C
p C
c
I
y y
y A
 

11. Example(1)
CH.3: Hydrostatic Forces on Plane Surfaces

12. Example(2)
CH.3: Hydrostatic Forces on Plane Surfaces

13. Hydrostatic Forces on Curved Surfaces
CH.3: Hydrostatic Forces on Plane Surfaces
 FR on a curved surface is more involved since it requires
integration of the pressure forces that change direction
along the surface.
 Easiest approach: determine horizontal and vertical
components FH and FV separately.

14. Hydrostatic Forces on Curved Surfaces
CH.3: Hydrostatic Forces on Plane Surfaces
 Horizontal force component on curved surface: FH=Fx. Line of action
on vertical plane gives y coordinate of center of pressure on curved
surface.
 Vertical force component on curved surface: FV=Fy+W, where W is
the weight of the liquid in the enclosed block W=rg. X coordinate of
the center of pressure is a combination of line of action on horizontal
plane (centroid of area) and line of action through volume (centroid of
volume).
 Magnitude of force FR=(FH
2+FV
2)1/2
 Angle of force is a = tan-1(FV/FH)

15. Example(3)
CH.3: Hydrostatic Forces on Plane Surfaces

16. Example(3)
CH.3: Hydrostatic Forces on Plane Surfaces

17. Example(4)
CH.3: Hydrostatic Forces on Plane Surfaces

18. Example(5)
CH.3: Hydrostatic Forces on Plane Surfaces

19. Example(6)
CH.3: Hydrostatic Forces on Plane Surfaces

20. Example(7)
CH.3: Hydrostatic Forces on Plane Surfaces

21. Post test
-
CH.3: Hydrostatic Forces on Plane Surfaces
Q1)) (5 marks)
Gate AB in Fig. below is 16 ft long and 8 ft wide.
Neglecting the weight of the gate, compute the
water level h for which the gate will start to fall.
Q2)) (5 marks)
Gate AB in Fig. below a is 16 ft long and 8 ft
wide. Neglecting the weight of the gate,
compute the water level h for which the gate
will start to fall.

22. Answer key
CH.3: Hydrostatic Forces on Plane Surfaces
Pretest
Q1))

23. Answer key
CH.3: Hydrostatic Forces on Plane Surfaces
Pretest
Q2))

24. Answer key
CH.3: Hydrostatic Forces on Plane Surfaces
Post test
Q1))

25. Answer key
CH.3: Hydrostatic Forces on Plane Surfaces
Post test
Q2))

26. References
CH1: Fluid Properties
1. Evett, J., B. and Liu, C. 1989 “2500 solved problems in fluid mechanics and
hydraulics” Library of Congress Cataloging- in-Publication Data, (Schaum's
solved problems series) ISBN 0-07-019783-0
2. Rajput, R.,K. 2000 “ A Text Book of Fluid Mechanics and Hydraulic
Machines”. S.Chand & Company LTD.
3. White, F., M. 2000 “ Fluid Mechanics”. McGraw-Hill Series in Mechanical
Engineering.
4. Wily, S., 1983 “ Fluid Mechanics”. McGraw-Hill Series in Mechanical
Engineering.