Force on submerged surfaces can either be on an inclined or a horizontal plane. A body submerged in a fluid always has a force acting on it due to hydrostatic pressure. As such, these forces are known as hydrostatic forces. A single surface point of force emanates from a planar (Falkovich 22). The process is mechanically equivalent to the pressure on the load distributed along the whole pack. For instance, taking the resultant force to be M, M tends to compress towards the normal surface of a point termed as the center of pressure.
The hydrostatic force on a curved surface is also available. For a curved surface, it is impossible to obtain the equivalent single resultant force of the load. In such a case we make use of inclined or horizontal planes (Falkovich 30). For an horizontal plane the resultant force is the same as the resultant force of the planar component. Additionally, for an inclined/vertical plane, it is possible to obtain the weight of the volume of the fluid between the surfaces and that becomes the force of an inclined plane or a vertical one.
The center of pressure’s description emanates from the principal of moments which states that: moments of resultant force about an axis is equal to the sum of moments of the components about the same axis (Song et al. 62).
Carrying Out Appropriate Calculations on Force and Centre of Pressure on Submerged Surfaces
1. Force on a planar surface
Using figure 1 to calculate the parameters
YCP YK
XK
XCP
Figure 1
To get the appropriate calculations of the force we use the following parameters.
M= XYkA
Where
X; fluid specific gravity
Yk; the centroid
A; surface area
XYk multiplying the fluid specific gravity and the centroid gives us the hydrostatic pressure of the fluid at a depth of the surface.
The planar surface also has two conditions;
a. Under normal atmospheric pressure, the equation XYk is the appropriate to calculate force.
b. If there is additional pressure, we make use of the equation below to calculate for force
Yk+p/X
Where p is the additional pressure.
So since in a planar surface is where the resultant force tends to compress towards the center of pressure. So to get the center of pressure we use the principle of moments.
For example, let the center of pressure be B
So the coordinates of B will be (X, Y)
A coordinate system with the centroid being the origin is
X=IXY/ Yk A and Y=IXX/YKA
IXY; area of moment of inertia
IXX; product of inertia
And since IXX
is equivalent to zero, so X is also zero hence the center of pressure for a planar surface is at the centroid.
2. Center of pressure for curved surfaces.
Using figure 2
b A
h
Hh *
dh
g
p B
Center of pressure for a curved region
Using principal of moments
The moment force about a free surface of a fluid is,
dF x h
pgh x b x dh x h
this is because dF is pgh x b x dh
the sum of all moments of force
pgh x b x dh x h = pg h x b x hdh
pg bh2dh = pg h2dA
h2dA= bh2dh
IO is the moment of inertia
Then pg IO is the sum of the moments of inertia.
So force acting on p at a distance h is given by,
F= h*= pgh IO
F=pgAH
H*=
IO=IG+A+H2
Replacing the product of momentum to the equation, the center of pressure becomes
*=
Determining the Parameters of Hydraulic Devices Used in Transmission of Force
Hydraulics are primarily based on the Pascal law and Bernoulli’s law of hydraulics. It basically deals with the flow of fluids.
Pascal principal is based on the increase of force. It postulates that applying a small force to a small piston of a cylinder enables transmission through a tube to a large cylinder which presses the piston equally at all sides of the cylinder including the large piston (Kumar, Shravan and Prashanth 2460). Bernoulli’s principal, on the other hand, states that energy in a fluid is due to elevation, pressure, and motion, and if there are no losses due to friction and no work done, the sum of the energies remains constant (Falkovich 51). Thus, velocity energy, deriving from motion, can be partly converted to pressure energy by enlarging the cross section of a pipe, which slows down the flow but increases the area against which the fluid is pressing. These are two principals governing the operation of hydraulic devices in the transmission of force and pressure.
Parameters included are
1. Driver
2. Pump
3. Motor
4. Control valves
5. load
Each parameter hasa distinct use. The driver acts as an electrical motor conversion of electrical energy to the mechanical energy, and also serves as an engine. The pump increases the pressure. The motor is basically a conversion device but in this case hydraulic to mechanical. It produces a reciprocating load. Therefore, fluid power provides more tons of force compared to other systems.
Works Cited
Falkovich, Gregory. Fluid mechanics. Cambridge University Press, 2018.
Kumar, Mr K. Shravan, and B. Prashanth. "Design " Fabrication of hydraulic press." International journal of scientific development and research 2 (2017): 2455-2631.
