CE 332(HYDRAULICS)
BSCE-3A/3B
HYDROSTATIC FORCE ON IMMERSED SURFACES
I. LEARNING OUTCOME:
• Evaluate the vertical force acting on a horizontal surface immersed in liquid.
• Develop equation to evaluate the total horizontal pressure acting on a vertical surface immersed
in a liquid.
• Develop equation to evaluate the pressure force acting on an inclined surface immersed in a
liquid.
II. DISCUSSION:
Immersed surfaces are subject to hydrostatic pressures. The deeper the surface below the fluid surface, the
greater the intensity of the pressure. The pressure varies linearly with depth if the fluid is incompressible.
The immersed surface may generally be horizontal, vertical or inclined.
A. HORIZONTAL SURFACE
Consider a horizontal surface immersed in a liquid. The total weight of the fluid above this surface is
equal to the volume of the liquid above the surface multiplied by the specific weight of the liquid. The
immersed surface is, thus, subject to a vertical force equal to the total eight of the fluid above it.
Therefore,
𝑭 = 𝜸𝑨𝒉
Where F is the force acting on the immersed surface, γ is the specific weight of the liquid, A is the area of
the surface, and h is the depth of the horizontal surface measured from the liquid surface.
Example:
Calculate the total force acting on the base of a square tank 4 ft. long and contains water to a depth of 3 ft.
Solution:
Area = 4ft(4ft) = 16ft2
𝑭 = 𝜸𝑨𝒉 = 𝟔𝟐. 𝟒 𝒍𝒃𝒔/𝒇𝒕³(𝟑𝒇𝒕)
𝑭 = 𝟐𝟗𝟗𝟓. 𝟐 𝒍𝒃
B. VERTICAL SURFACE & INCLINED SURFACE
VERTICAL SURFACE:
As previously stated, the pressure varies with depth below the liquid surface. Therefore, a vertically
immersed surface will be subject to different pressure heads according to the point of interest. Consider a
vertical plane surface immersed in a liquid.
, INCLINED SURFACE:
Consider now the more general case in which the submerged plane surface is inclined by an angle Ɵ with
the liquid surface. The area can have an arbitrary shape. The objective is to determine the direction,
location, and magnitude of the resultant force acting on one side of the area.
For horizontal plane surface submerged in liquid, or plane surface inside a gas chamber, or any plane
surface under the action of uniform hydrostatic pressure, the total hydrostatic force is given by
where p is the uniform pressure and A is the area.
In general, the total hydrostatic pressure on any plane surface is equal to the product of the area of the
surface and the unit pressure at its center of gravity.
where pcg is the pressure at the center of gravity. For homogeneous free liquid at rest, the equation can be
expressed in terms of unit weight γ of the liquid.
̅ is the depth of liquid above the centroid of the submerged area.
Where 𝒉
Derivation of Formulas
The figure shown below is an inclined plane surface submerged in a liquid. The total area of the plane
surface is given by A, cg is the center of gravity, and cp is the center of pressure.
BSCE-3A/3B
HYDROSTATIC FORCE ON IMMERSED SURFACES
I. LEARNING OUTCOME:
• Evaluate the vertical force acting on a horizontal surface immersed in liquid.
• Develop equation to evaluate the total horizontal pressure acting on a vertical surface immersed
in a liquid.
• Develop equation to evaluate the pressure force acting on an inclined surface immersed in a
liquid.
II. DISCUSSION:
Immersed surfaces are subject to hydrostatic pressures. The deeper the surface below the fluid surface, the
greater the intensity of the pressure. The pressure varies linearly with depth if the fluid is incompressible.
The immersed surface may generally be horizontal, vertical or inclined.
A. HORIZONTAL SURFACE
Consider a horizontal surface immersed in a liquid. The total weight of the fluid above this surface is
equal to the volume of the liquid above the surface multiplied by the specific weight of the liquid. The
immersed surface is, thus, subject to a vertical force equal to the total eight of the fluid above it.
Therefore,
𝑭 = 𝜸𝑨𝒉
Where F is the force acting on the immersed surface, γ is the specific weight of the liquid, A is the area of
the surface, and h is the depth of the horizontal surface measured from the liquid surface.
Example:
Calculate the total force acting on the base of a square tank 4 ft. long and contains water to a depth of 3 ft.
Solution:
Area = 4ft(4ft) = 16ft2
𝑭 = 𝜸𝑨𝒉 = 𝟔𝟐. 𝟒 𝒍𝒃𝒔/𝒇𝒕³(𝟑𝒇𝒕)
𝑭 = 𝟐𝟗𝟗𝟓. 𝟐 𝒍𝒃
B. VERTICAL SURFACE & INCLINED SURFACE
VERTICAL SURFACE:
As previously stated, the pressure varies with depth below the liquid surface. Therefore, a vertically
immersed surface will be subject to different pressure heads according to the point of interest. Consider a
vertical plane surface immersed in a liquid.
, INCLINED SURFACE:
Consider now the more general case in which the submerged plane surface is inclined by an angle Ɵ with
the liquid surface. The area can have an arbitrary shape. The objective is to determine the direction,
location, and magnitude of the resultant force acting on one side of the area.
For horizontal plane surface submerged in liquid, or plane surface inside a gas chamber, or any plane
surface under the action of uniform hydrostatic pressure, the total hydrostatic force is given by
where p is the uniform pressure and A is the area.
In general, the total hydrostatic pressure on any plane surface is equal to the product of the area of the
surface and the unit pressure at its center of gravity.
where pcg is the pressure at the center of gravity. For homogeneous free liquid at rest, the equation can be
expressed in terms of unit weight γ of the liquid.
̅ is the depth of liquid above the centroid of the submerged area.
Where 𝒉
Derivation of Formulas
The figure shown below is an inclined plane surface submerged in a liquid. The total area of the plane
surface is given by A, cg is the center of gravity, and cp is the center of pressure.
