Fluid Statics

Introduction

The Fluid that is at rest, there is no shear stress can be found. It is exerting a force from normal to a solid barrier; it is referred to as a motion phenomenon, which is important to determine the pressure at varying levels of the atmosphere. This Fluid Static theory is evolved for calculating the force on submerged materials like parts of ships and submarines, including the force measurement of hydraulic systems and dams.

Definition of Fluid Statics

A part of Fluid Mechanics, dealing with fluids while no motion of particles is present between the fluids, is called Fluid Statics. It occurs in two distinctive situations, such as when there is no motion and while moving like a rigid solid. According to Pascal’s principle, the pressure can be transmitted by static fluids. Similarly, in Archimedes’ point of view, it can be explained that a buoyant object is the same as the displaced liquid’s weight. The motion of gasses and liquids are known as fluid kinematics, and the measurement of the forces when fluid is in  motion is called Fluid dynamics. fluid statics deals with the response or behavior of the fluid when it is at rest.

Dealing Factors of Fluid Statics

The Fluid Statics deals with the intensity of pressure, mass, friction between fluid molecules.

Mass density: mass density refers to the volume of an object; it depends on the weight of individual atoms or molecules which build an object. On the other hand, a solid object or hollow object’s weight. In order to liquids or solids, both have individual mass density. Such as, the solid object’s weight can be measured as 1000kg/m3, and a high-density object, such as gold is about 20 times larger than the liquids, whereas the gasses are equal with water density. In terms of measuring gravity, the densities have been calculated. The density of water at 4 degrees celsius is used to measure the ratio of an object’s density because, at 4 degrees celsius, water becomes very dense. Due to the temperature and pressure, the density of an object changed.

Pressure: an object’s density depends on the pressure; it can be defined that pressure is the activity of force that measures the area of surface at a perpendicular act. 

“Pressure = force applied to the perpendicular to the surface/ area of the surface”

Pressure can be measured by using several units, such as Pascal, atmospheres, pounds, per square inch, millibars. To measure the pressure two pressure gauges have been used, “open-tube manometer and closed-tube manometer”. It compares the pressure of an unknown point with the known point pressure. A Closed-tube manometer, sealed at one point which is close to zero pressure and another part open to the atmosphere, is also known as a mercury barometer. It helps to calculate the difference between two-end side pressures of a tube, and the fluid’s density can easily be measured through this unit.

On the other hand, the open-tube manometer is used to measure the pressure of a region, in which one side of this is close to the atmosphere and another is connected with the region. Here, the height of the tube in which the fluid is at rest is proportionate to the pressure difference. There are several kinds of pressure with which Fluid Statics deals, such as, “atmospheric, gauge, vacuum or negative and absolute pressure”. 

Examples of Fluids Statics

Problem: “A dam has a surface area of 50.0km2 and an average depth of 40.0m. What mass of water is held behind the dam?”

Solution: the density of water can be termed as “ρ”, the mass is “m” and volume is “V”, according to the formula, ρ = m/V, 

Therefore, mass = density of water * Volume

Where, the surface area of the reservoir is “A” and average depth is “h”. 

V = Ah

      = 50.0km2 * 40.0m 

     = {(50.0km2) * (103m / 1km)2} * 40.0m 

    = 2.00*109m3

And the density of water is given 1.000 * 103 kg/m3

Mass = (1.00*103 kg/m3) * (2.00*109m3)

=2.00*1012 kg

Therefore, the force that the dam supplies are smaller than water density along with weight

Pascal’s Principle

According to French scientist Blaise Pascal, when fluids are at rest, the pressure at any point in fluids remains the same in all directions. He stated that in a hydraulic system, the exerted pressure is equal to each piston. As per the law, the formula is followed to measure the pressure of fluids is:

“Force = Pressure transmitted * cross-sectional Area”

The principle of Pascal refers to the total pressure in a fluid that will be equal to the pressures exerted from all the different edges of the wall of an enclosed container. 

Conclusion

Depending on pressure measurement, Fluid Statics refers to the calculation of pressure at any point, which remains the same. On the other hand, it describes the pressure at the vessel wall which is perpendicular. Fluid Statics explains the mathematical measurement of substances.