Hydrostatic Force

# Hydrostatic Force - Mechanical Engineering SSC JE (Technical)

HYDROSTATIC FORCE

• Pressure Force on Plane Surfaces 
• Pressure force always acts normal to plane surface. 
• The center of pressure passes through centroid of the pressure diagram. 
• In horizontal plane surface pressure force passes through centroid of area whereas in inclined and vertical plane surfaces pressure force passes below the centroid of the area. 
• The total pressure force on plane area is
F = Area × Pressure at the centroid

where,  = vertical depth of centroid of area from free liquid surface A = Area of surface 
• Depth of center of pressure from free surface is given by

where, IG = Moment of inertia about centre of gravity of the body. 

• Center of pressure always lies below the centroid of the area in non-horizontal surfaces. 
• The depth of center of pressure on inclined plane is given by

• Pressure Force on curved surfaces: Horizontal component of the resultant hydrostatic force 'Fx' of curved surface may be computed by projecting the surface upon a vertical plane and multiplying the projected area by the pressure at its own centre of area. 
• Vertical component of force 'Fy' is equal to the weight of the liquid block lying above the curved surface upto free surface.
• Resultant Force
• Angle of line of action of resultant force with the horizontal is given by tan
• Depth of center of pressure for some vertical plane surfaces

1. RECTANGLE

2. TRAPEZIUM

3. TRIANGLE

4. CIRCLE

5. SEMI CIRCLE

6. PARABOLA

• Archimedes principle and Force of buoyancy
• When a body is submerged either fully or partially then it is acted upon by a force of buoyancy vertically up ward which is equal to weight of liquid displaced by the body. This force of buoyancy always acts through the centroid of liquid displaced. 
• Stability of submerged bodies
If centre of buoyancy (B) and centre of gravity (G), coincide then submerged body is in neutral equilibrium & if  B is above G it will be in stable equilibrium.
If B is below G it will be in unstable equilibrium.

• Stability of floating bodies: The stability of floating body is defined by relative position of metacentre (M) and centre of gravity (G).
If M lies above G (GM ve) then it is stable equilibrium
If M lies below G (GM  - ve) then unstable equilibrium
If M coincides with G (GM  0) then neutral equilibrium
é =+ù êú êú ê =ú êú êú êë =úû

where GM = metacentric height.
I = moment of inertia about longitudinal axis of the plane at the level of free surface. ('I' is minimum moment of inertial of the plane.) V = Volume of liquid displaced by the body.
BG = Distance between centroid of liquid displaced and centroid of the body.
• For stable equilibrium of a circular cone floating with its apex downward having diameter 'd' and a vertical height 'h'. (The specific gravity of the cone is 'S') the condition for stability is

Depth of submergence is x = S1/3h
• If a floating body oscillates then its time period of transverse oscillation is given by
• Vortex Motion :
A whirling mass of fluid is called vortex flow.
(i) Forced Vortex Flow: 
• When a fluid is rotated about a vertical axis at constant speed, such every particle of its has the same angular velocity, motion is known as the forced vortex. Forced vortex requires constant supply of external energy/torque.

where h is height of paraboloid, and r is radius of paraboloid at top.
Volume of paraboloid

= ½ of volume of circumscribing cylinder.

• The surface profile of forced vortex flow is parabolic.
Example of forced vortex flow is rotating cylinder & flow inside centrifugal pump.

(ii) Free Vortex Flow: 
• In this flow fluid mass rotates due to conservation of angular momentum. No external torque or energy is required. In free vortex flow Bernoulli's equation can be applied.  The velocity profile is inversely proportional with the radius.
v r = constant
The point at the centre of rotation is called singular point, where velocity approaches to infinite.
Example of free vortex motion are whirling mass of liquid in wash basin, whirlpool in rivers etc.
The document Hydrostatic Force | Mechanical Engineering SSC JE (Technical) is a part of the Mechanical Engineering Course Mechanical Engineering SSC JE (Technical).
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## FAQs on Hydrostatic Force - Mechanical Engineering SSC JE (Technical)

 1. What is hydrostatic force in mechanical engineering?
Ans. Hydrostatic force in mechanical engineering refers to the force exerted by a fluid on a submerged or partially submerged object. It is a result of the pressure exerted by the fluid on the object's surface due to its weight. This force is typically calculated using the formula F = ρghA, where ρ is the density of the fluid, g is the acceleration due to gravity, h is the height of the fluid column, and A is the area of the object's surface.
 2. How does hydrostatic force affect the stability of a structure?
Ans. Hydrostatic force plays a crucial role in determining the stability of a structure, especially those that are submerged in fluid or come into contact with fluid. If the hydrostatic force acting on the structure's submerged surface is greater than the weight of the structure, it will experience an upward force, known as buoyant force, which contributes to the stability. On the other hand, if the hydrostatic force is less than the weight, the structure may experience a downward force and become unstable.
 3. What are some practical applications of hydrostatic force in mechanical engineering?
Ans. Hydrostatic force is widely applicable in various areas of mechanical engineering. Some practical applications include: - Designing and analyzing hydraulic systems, such as hydraulic lifts and presses, where hydrostatic force is utilized to generate mechanical power. - Determining the stability and buoyancy of ships, submarines, and offshore structures to ensure their safe operation in water. - Calculating the forces exerted on dams and retaining walls due to water pressure to ensure their structural integrity. - Designing and analyzing piping systems, such as water distribution networks, where hydrostatic force is considered to prevent leakage and ensure proper flow. - Assessing the stability and safety of underwater pipelines and cables by evaluating the hydrostatic forces acting on them.
 4. How can hydrostatic force be calculated for irregularly shaped objects?
Ans. Hydrostatic force can be calculated for irregularly shaped objects by integrating the pressure distribution over the object's surface. This involves dividing the surface into small elemental areas and calculating the pressure at each point using the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the vertical distance from the surface to the fluid level. By summing up the pressure contributions from all elemental areas, the total hydrostatic force can be determined.
 5. What are the factors that affect the magnitude of hydrostatic force?
Ans. The magnitude of hydrostatic force is influenced by several factors, including: - The density of the fluid: A denser fluid will exert a greater hydrostatic force compared to a less dense fluid. - The height of the fluid column: The greater the height of the fluid column, the higher the hydrostatic force. - The area of the object's surface: A larger surface area will result in a greater hydrostatic force. - The orientation of the object: The angle at which the object is submerged or partially submerged in the fluid can affect the distribution of hydrostatic force on its surface. - The shape of the object: Irregularly shaped objects may experience variations in hydrostatic force due to variations in pressure distribution across their surfaces.

## Mechanical Engineering SSC JE (Technical)

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## Mechanical Engineering SSC JE (Technical)

6 videos|97 docs|57 tests

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