This document discusses hydrostatic forces on plane and curved surfaces. It explains that the total force on a vertical plane surface is the sum of the forces due to pressure at different depths. The force is equal to pressure times area. For curved surfaces, the horizontal and vertical force components must be calculated separately, then combined into a resultant force. The center of pressure is also introduced, which is the point where the total hydrostatic force can be considered to act. Examples are provided to calculate hydrostatic forces on different surfaces.

1. Fluid mechanics
Lecture 4
Dr. Ahmed Adel Saleh

2. Contents
• Pressure Variation in a Static Fluid
• Pressure Measurement
• Hydrostatic Force on a Plane Surface
• Hydrostatic Force on a Curved Surface

3. What are Hydrostatic Forces ?
• Force due to the pressure of a fluid at rest
• Ex:
• Force exerted on the wall of storage tanks, dams, and ships)

4. Why study Hydrostatic Forces ?

5. Previously, we learned
• Pressure affects perpendicular to the surface upon which it acts.
• Pressure increases linearly dependent only to the vertical depth
• Pressure on horizontal surfaces (i.e., at the bottom of tanks) is uniform
• Pressure depends on specific weight of the fluid

6. Hydrostatic Forces on
Plane Surfaces

7. newindianexpress.com

9. Total force acts on vertical straight surface
F1
F2
h1 = 4 m2 m
F1 = γ h1 Agate
F1 = 9.8 * 4 * (2*2) = 156.8 KN
h2 = 2 m
F2 = 0.5* γ h2 Agate
F2 = 0.5*9.8 * 2 * (2*2) = 39.2 KN
FR = F1 + F2
FR = 196 kN
(special case)

10. In-class exercise
h1
h2
h3
Square gate
Assume heights [h1(1:4), h2 (1:3)]
γwater = 9.8 kN/m3
Find force needed to start drain (i.e., open the gate)

11. The Hydrostatic Pressure Distribution
(General case)
x
y
z
x
y
Θ

12. Force Caused by a Hydrostatic Pressure Distribution
Force Caused by a
Hydrostatic Pressure
Distribution
Magnitude of
resultant hydrostatic
force
Location of affect of
the resultant
hydrostatic force

13. Force Caused by a Hydrostatic Pressure Distribution 2
1st moment of area
pressure at centroid of A
Magnitude of resultant hydrostatic force on plane surface is
product of pressure at centroid of area and area of surface.
F = γ hc A

14. The Center of Pressure for a Hydrostatic Pressure Distribution
by taking moments about horizontal axis 0-0
2nd moment of area about 0-0
= moment of inertia
about 0-0 about centroidal axis

15. The Center of Pressure for a Hydrostatic Pressure Distribution
The Center of Pressure is always below centroid

16. The Center of Pressure for a Hydrostatic Pressure Distribution
Determine xcp by taking moment about y axis
For symmetry surfaces

17. In-class exercise 2
(General case)
Square gate (2m)
γwater = 9.8 kN/m3
Find force needed to raise the gate (neglect gate weight
and coefficient of friction)
Θ = 30°
4.0 m
1. Find depth of centroid (hc)
2. Find Hz forces (F = γ hc A)

18. Special cases
F = γ h A

19. Hydrostatic Forces on Curved
Surfaces

20. • For the case of a curved surface, all elements do not lie in the same
plane. So the hydrostatic forces (although perpendicular to their
respective elements) do not form a system of parallel forces.
• To get the hydrostatic force on a submerged curved surface, both
horizontal and vertical components are calculated first. Then, their
resultant will be the required force.

23. • Pressure at a point in a fluid
• Proof that pressure acts equally in all directions
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24. Hydrostatic Force on a Plane Surface
• How much is the resultant force on inclined submerged surface ?
• Where that resultant force act ?
This section explains how to represent hydrostatic pressure
distributions on one face of a panel with a resultant
force that passes through a point called the center of pressure.
This information is relevant to applications such
as dams and water towers.

26. • The force on an elemental plane lamina equals the pressure at the
depth of the element multiplied by its area,
www.engineersedge.com

27. Success at solving problems of
fluid mechanics

28. • https://www.youtube.com/watch?v=2ssodW8tVSA