Fluid Statics and Its Application

Table of Contents

Fluid Statics and Fluid Dynamics are the two branches of Fluid Mechanics or Fluid Flow Operations.

Fluid Statics deals with the fluid at rest condition and Fluid Dynamics is the study of the fluid in dynamic condition.

Difference Between Fluid Statics and Fluid Dynamics

Fluid Statics

The study of fluids at static (rest) conditions is called Fluid Statics.

Fluid statics, also known as hydrostatics, deals with the study of fluids at rest or in equilibrium. In other words, it examines the behavior of fluids when they are not in motion.

Fluid statics is concerned with pressure distribution within a fluid, buoyancy, stability of floating objects, and pressure variations with depth in a fluid (hydrostatic pressure).

Examples of applications include calculating the buoyant force on a submerged object, designing dam structures, and understanding the pressure distribution in a fluid container.

Fluid Dynamics

The study of fluids in motion relative to stationary solid walls is called Fluid Dynamics.

Fluid dynamics, also known as hydrodynamics, is the branch of fluid mechanics that deals with the study of fluids in motion. It examines how fluids behave when they flow and interact with their surroundings.

This branch of fluid mechanics is concerned with phenomena such as fluid flow patterns, turbulence, drag forces, lift forces, and the study of fluid behavior in pipes, channels, and around objects in motion (e.g., aircraft, ships).

Examples of applications include designing aerodynamic shapes for aircraft, optimizing the flow of fluids in pipelines, and understanding the behavior of ocean currents.

Importance of Fluid Flow Operations in Chemical Engineering

Understanding fluids and their flow is important to deal with the problems based on the movement of fluids through the pipes, pumps, fans, blowers, and all kinds of process equipment.

Fluid flow operations are also important to study heat flow and separation operations that depend on diffusion and mass transfer operations.

Nature of Fluid/Definition of Fluid

A fluid is a substance that does not permanently resist distortion.

A fluid is a substance that is capable of flowing if allowed to do so.

An attempt to change the shape of a mass of fluid results in layers of fluid sliding over one another until a new shape is attained. This means a fluid has no definite shape of its own, but it confirms the shape of the containing vessel.

During the change in shape shear stress exists, the magnitude of which depends on the viscosity of the fluid and the rate of sliding, but when the final shape has been reached, all shear stress will have disappeared.

A fluid is a substance that undergoes continuous deformation when subjected to a shearing force.

A fluid that is in equilibrium is free from shear stresses.

Liquids, gases/vapours possess the above-cited characteristics, they are referred to as fluids.

Properties of Fluid

Density

The density or mass density of a fluid is the mass of the fluid per unit volume.

It is designated by the symbol “ρ“.

In the SI system, it is expressed in kg/m³.

The density of pure water at 277 K (4^oC) is taken as 1000 kg/m³.

Specific Volume

A specific volume of a fluid is the volume of the fluid per unit mass.

In the SI system, it is expressed in m³/kg.

Weight Density

The weight density of a fluid is the weight of the fluid per unit volume.

In the SI system, it is expressed in N/m³.

The specific weight or weight density of pure water at 277 K (4^oC) is taken as 9810 N/m³.

The relation between mass density and weight density is

w = ρ g

Where g is the acceleration due to gravity (9.81m/s²).

Specific Gravity

The specific gravity of a fluid is the ratio of the density of the fluid to the density of a standard fluid.

For liquids, water at 277 K (4^oC) is considered as a standard fluid and for gases, air at NTP (0^oC and 760 torr) is considered as a standard fluid.

Vapour Pressure

The vapour pressure of a pure liquid is defined as the absolute pressure at which the liquid and its vapour are in equilibrium at a given temperature or the pressure exerted by the vapour (on the surface of a liquid) at equilibrium conditions is called the vapour pressure of the liquid at a given temperature.

Pure air-free water exerts a vapour pressure of 101.325 kPa (760 torr) at 373.15 K (100^oC).

Surface Tension

The property of liquid surface film to exert tension is called as surface tension.

It is the force required to maintain a unit length of film in equilibrium.

It is denoted by the symbol “σ” and its SI unit is N/m.

Viscosity

A fluid undergoes continuous deformation when subjected to a shear stress.

The resistance offered by a fluid to its continuous deformation is called viscosity.

In the SI system, it has the units of (N.s)/m² or Pa.s or kg/(m.s).

Classification Fluid

Based on resistance to flow

▶ Ideal Fluid

▶ Real Fluid

Based upon the behavior of fluids under the action of externally applied pressure and temperature.

▶ Compressible Fluids

▶ Incompressible Fluids.

Based upon the behavior of fluids under the action of shear stress

▶ Newtonian Fluids

▶ Non-Newtonian Fluids.

Ideal Fluid and Real Fluid

Ideal Fluid

It is a fluid that does not offer resistance to flow. Which means it has no viscosity and it is frictionless and incompressible.

However, an ideal fluid does not exist in nature and therefore, it is only an imaginary fluid.

An ideal fluid offers no resistance to flow or change in shape.

Real Fluid

It is a fluid that offers resistance when it is set in motion.

All naturally occurring fluids are real fluids.

Compressible and Incompressible Fluid

At a given temperature and pressure, a fluid possesses a definite density, which in engineering practice is usually measured in kilograms per cubic meter.

Although the density of all fluids depends on the temperature and pressure, the variation in density with changes in these variables may be small or large.

If the density changes only slightly with a moderate change in temperature and pressure, the fluid is said to be incompressible.

If the density change is significant with moderate change in temperature and pressure, the fluid is said to be compressible.

All liquids are generally considered incompressible and all gases are compressible.

Terms are relative, however, and the density of the liquid can change appreciably if pressure and temperature are changed over a wide limit.

Also, gases subjected to small percentage changes in pressure and temperature act as incompressible fluids, the density changes under such conditions may be neglected without serious error.

Read Also: Fluid Flow Operations

Pressure Concept

The basic property of a static fluid is pressure.

Pressure is a surface force applied by a fluid towards the container walls.

At every point within a volume of fluid pressure exists.

For a static fluid, pressure is independent of the direction of any internal surface on which the pressure is assumed to act.

Pressure Concept-Forces on static element of fluid — Figure 1: Pressure Concept – Forces on Static Element of Fluid

Choose any point 0 in a mass of static fluid and, as shown in Fig. 1.

Construct a cartesian system of coordinate axes with 0 as the origin.

The x-axis and y-axis are in the horizontal plane, and the z-axis points vertically upward.

Construct a plane ABC cutting the x, y, and z axes at distances from the origin of Δx, Δy, and Δz respectively.

Planes ABC, AOC, COB, and AOB form a tetrahedron (a triangular pyramid).

Let, θ be the angle between planes ABC and COB. This angle is less than 90° but otherwise is chosen at random.

Imagine that the tetrahedron is isolated as a free body and consider all forces acting on it in the direction of the z-axis, either from outside the fluid or from the surrounding fluid.

Three forces are involved:
(1) The force of gravity acting downward,
(2) The pressure force on plane COB acting upward, and
(3) The vertical component of the pressure force on plane ABC acting downward.

Since the fluid is in equilibrium, the resultant of these forces is zero. Also, since fluid in equilibrium cannot support shear stresses, all pressure forces are normal to the surface on which they act.

Otherwise, there would be shear-force components parallel to the faces.

The area of face COB is (Δx Δy)/2.

Let, the average pressure on this face be $\bar{p}_z$ .

Then the upward force on the face is $\bar{p}_z \Delta x \Delta y /2$ .

Let, $\bar{p}$ be the average pressure on face ABC.

The area of this face is $\Delta x \; \Delta y \; /(2 \; cos\theta )$ , and the total force on the face is $\bar{p} \Delta x \Delta y (2 cos \theta)$ .

The angle between the force vector of pressure $\bar{p}$ with the z-axis is also $\theta$ , so the vertical component of this force acting downward is

(1) $\begin{equation*} \frac{\bar{p} \Delta x \; \Delta y \;cos \theta}{2 \; cos \theta} = \frac{\bar{p}\; \Delta x \Delta y }{2} \end{equation*}$

The volume of the tetrahedron is $\Delta x \Delta y \Delta z/6$ .

If the fluid density is $\rho$ , the force of gravity acting on the fluid in the tetrahedron is $\rho \Delta x \Delta y \Delta z g/6 g_c$ .

This component acts downward. The force balance in the z direction becomes

(2) $\begin{equation*} \frac{\bar{p}_z \Delta x \; \Delta y}{2} - \frac{\bar{p}\Delta x \Delta y}{2} - \frac{\rho \Delta x \Delta y \Delta z g}{6 g_c} = 0 \end{equation*}$

Dividing by $\Delta x \Delta y$ gives

(3) $\begin{equation*} \frac{\bar{p}_z}{2}-\frac{\bar{p}}{2}-\frac{\rho \Delta z g}{6 g_c}=0 \end{equation*}$

Now, keeping angle $\theta$ constant, let plane ABC move toward the origin 0.

As the distance between ABC and 0 approaches zero as a limit, $\Delta z$ approaches zero also and the gravity term vanishes.

Also, the average pressures $\bar{p}$ and $\bar{p}_z$ , approach p and $p_z$ , the local pressures at point 0, and Eq. (3) show that $p_z$ , becomes equal to p.

Force balances parallel to the x and y axes can also be written. Each gives an equation like Eq. (3) but containing no gravity term and in the limit

$p_x = p_y = p_z = P$

Since, both point 0 and angle $\theta$ were chosen at random, the pressure at any
point is independent of direction.

Applications of Fluid Statics in Chemical Engineering

Fluid statics plays a significant role in various aspects of chemical engineering. Here are some practical applications:

Tank Design and Sizing: Chemical plants often involve the storage and handling of liquids and gases. Fluid statics principles are used to design tanks, ensuring they can handle the weight and pressure of the stored substances without leaking or failing.

Pressure Vessels: Chemical reactions or processes might require high-pressure environments. Understanding fluid statics helps engineers design and construct pressure vessels that can safely contain and handle these high-pressure conditions.

Piping Systems: Fluid statics is crucial in designing piping systems for transporting liquids and gases within a chemical plant. Engineers consider the pressure distribution, fluid height, and forces exerted by static fluids to prevent leaks and optimize the system’s efficiency.

Mixing and Agitation: In many chemical processes, liquids need to be mixed or agitated. Fluid statics principles help in determining the pressure and force required for effective mixing while considering the behavior of fluids at rest.

Centrifuges: Centrifuges are used to separate components of a fluid mixture based on their density. Fluid statics principles help engineers optimize the design of centrifuges to achieve efficient separation.

Sedimentation Tanks: In wastewater treatment processes, sedimentation tanks are used to separate solid particles from liquid. Fluid statics principles guide the design of these tanks to ensure proper settling of solids.

Distillation Columns: Distillation is a common separation process in chemical engineering. Fluid statics is essential in designing distillation columns to ensure uniform distribution of liquids and vapor flow at various stages.

Liquid Level Measurement: Accurate measurement of liquid levels is critical in chemical processes. Fluid statics principles are employed in designing instruments such as pressure gauges, level sensors, and manometers for precise level measurement.

Chemical Reactors: Fluid statics help in designing reactors for chemical reactions involving liquids and gases. Proper pressure distribution and fluid behavior at rest are essential for safe and efficient reactions.

Heat Exchangers: Fluid statics is considered when designing heat exchangers that involve the transfer of heat between different fluids. Proper fluid distribution and pressure management contribute to efficient heat exchange.

Storage and Handling of Hazardous Materials: Chemical engineers need to ensure the safe storage and handling of hazardous substances. Fluid statics principles help in designing storage vessels and containment systems to prevent leaks and spills.

Hydraulic Systems: Fluid statics concepts are relevant in designing hydraulic systems used for moving and controlling fluids in chemical processes and equipment.

In chemical engineering, a strong understanding of fluid statics is crucial for designing equipment and processes that involve liquids and gases, ensuring their safe and efficient operation.

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Fluid Statics and its Application

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FAQ’s on Fluid Statics and Its Applications

What is a fluid?

A fluid is a substance that can flow and adapt to the shape of its container. It includes liquids and gases.

What is fluid statics?

Fluid statics, also known as hydrostatics, deals with fluids at rest and the forces exerted by fluids on surfaces in contact with them.

How do fluids behave in different containers?

Fluids take the shape of the container they are in, adapting to its volume and boundaries. This property is known as fluidity.

What is the difference between a liquid and a gas in terms of fluid statics?

Liquids are nearly incompressible and have definite volumes, while gases are highly compressible and fill their containers completely.

How is fluid statics relevant in engineering?

Fluid statics is crucial in designing pipelines, tanks, and reservoirs to ensure stability and prevent leakage. It’s also important in understanding the behavior of fluids in engineering systems.

Can fluids exert forces even when they’re not in motion?

Yes, fluids at rest can exert forces on surfaces they come in contact with due to the pressure they exert. This is the basis of fluid statics.

How does fluid statics relate to atmospheric pressure?

Atmospheric pressure is the pressure exerted by the weight of the air above us. It’s also a form of fluid pressure and follows similar principles as fluid statics.

Are fluid statics and fluid dynamics the same?

No, they’re different branches. Fluid statics deals with fluids at rest, while fluid dynamics studies the behavior of fluids in motion.

Is viscosity a part of fluid statics?

Viscosity, which refers to a fluid’s resistance to flow, is more associated with fluid dynamics than fluid statics.

What are the applications of fluid statics in everyday life?

Fluid statics principles are seen in the functioning of drinking straws, siphoning liquids, and even in how water levels are maintained in containers.

What are compressible fluids?

Compressible fluids, or compressible flow mediums, are those that can undergo significant changes in volume when subjected to changes in pressure and temperature, like gases.

What are ideal fluids and real fluids?

Ideal fluids are assumed to have no viscosity and follow idealized fluid dynamics principles. Real fluids, on the other hand, have viscosity and other real-world characteristics.

How is pressure distributed in a fluid at rest?

In a fluid at rest, pressure is transmitted equally in all directions. This is known as hydrostatic pressure distribution.

What is pressure head in fluid mechanics?

The pressure head is the height of a column of fluid that would create a specific pressure at its base. It’s used to quantify pressure in terms of a vertical distance.

How does pressure influence fluid flow in pipes and channels?

Pressure difference along a pipe or channel drives the fluid flow. Higher pressure at one end propels the fluid toward the lower-pressure end.

Process Design of Pump

Process Design of Piping

Thermodynamic Properties of Fluid

Laws of Thermodynamics